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The U.S. Supreme Court’s decision to overturn a Colorado court decision barring former President Donald J. Trump from the state’s primary ballot centers on the meaning of the Constitution’s 14th Amendment, which includes a clause disqualifying people who violated their oaths of office from holding government positions in the future.

The 14th Amendment was adopted in 1868 as part of the post-Civil War Reconstruction Era. To deal with the problem of former Confederates holding positions of government power, its third section disqualifies former government officials from holding office if they took an oath to support the Constitution but then betrayed it by engaging in an insurrection.

According to a Congressional Research Service report, a criminal conviction was not seen as necessary: federal prosecutors brought civil actions to oust officials who were former Confederates, and Congress refused to seat certain members under the clause. Congress passed amnesty laws in 1872 and 1898, lifting the penalties on former Confederates.

The Colorado Supreme Court concluded that Mr. Trump’s attempts to overturn his loss of the 2020 election, culminating in the Capitol riot on Jan. 6, 2021, made him an oath-breaking insurrectionist. It barred him from the state’s primary ballot. Mr. Trump’s lawyers appealed to the U.S. Supreme Court, which unanimously overturned the state decision.

All nine justices agreed that while states can enforce Section 3 against holders and seekers of state offices, they lack authority to enforce it against holders and seekers of national offices. The justice worried that otherwise, different states could reach different decisions about taking candidates off the ballot, resulting in a disruptive “patchwork” that would sever the link the framers wanted there to be between the federal government and the people of the United States as a whole.

The justices split, however, on what to say about the means by which federal officials could enforce Section 3 against federal office holders and seekers. Five justices in the majority said that it was necessary for Congress to enact legislation laying out procedures for doing so. The other four said addressing that question was unnecessary to resolve the case and criticized their colleagues for going farther and ruling out other potential mechanisms.

Other issues that arose during the briefings and arguments turned out not to be important in the Supreme Court’s handling of the issue. In particular, Mr. Trump’s legal team had argued that Section 3 did not apply to him on the theory that the phrase in the amendment “officer of the United States” should be interpreted as covering only appointed officials and not elected presidents. None of the justices embraced that reasoning.

Under its bright, frosty shell, Jupiter’s moon Europa is thought to harbor a salty ocean, making it a world that might be one of the most habitable places in our solar system.

But life as we know it needs oxygen. And it’s an open question whether Europa’s ocean has it.

Now, astronomers have nailed down how much of the molecule is made at the icy moon’s surface, which could be a source of oxygen for the waters below. Using data from NASA’s Juno mission, the results, published on Monday in the journal Nature Astronomy, suggest that the frozen world generates less oxygen than some astronomers may have hoped for.

“It’s on the lower end of what we would expect,” said Jamey Szalay, a plasma physicist at Princeton University who led the study. But “it’s not totally prohibitive” for habitability, he added.

On Earth, the photosynthesis of plants, plankton and bacteria pump oxygen into the atmosphere. But the process works differently on Europa. Charged particles from space bombard the moon’s icy crust, breaking down frozen water into hydrogen and oxygen molecules.

“The ice shell is like Europa’s lung,” Dr. Szalay said. “The surface, which is the same surface that protects the ocean underneath from harmful radiation, is, in a sense, breathing.”

Astronomers speculate that this oxygen might move into Europa’s watery underworld. If so, it could mix with volcanic material from the seafloor, creating “a chemical soup that may end up making life,” said Fran Bagenal, a planetary scientist at the University of Colorado Boulder.

The Juno orbiter, which launched in 2011 to discover what lies beneath Jupiter’s thick veil of clouds, is now on an extended mission exploring the planet’s rings and moons. Aboard the vehicle is an instrument called JADE, short for Jovian Auroral Distributions Experiment. Dr. Szalay’s team studied data collected by JADE as Juno flew through the plasma engulfing Europa.

But the team wasn’t directly looking for oxygen; it was counting hydrogen. Because the molecule is so light, all of the hydrogen produced at Europa’s surface floats high into the atmosphere. Oxygen, which is heavier, is more likely to hang lower or remain trapped in the ice.

But both molecules come from the same source: broken-down frozen H₂O.

“And so if we measure the hydrogen, we have a direct line to determine how much oxygen is produced,” Dr. Szalay said.

The team found that Europa’s surface generates about 13 to 40 pounds of oxygen each second. That’s over 1,000 tons per day, about enough to fill the Dallas Cowboys football stadium 100 times a year.

While earlier studies reported widely varying ranges, up to 2,245 pounds per second, this result shows the higher end of that range was unlikely. But according to Dr. Bagenal, this doesn’t necessarily harm Europa’s potential for habitability.

“We don’t really know how much oxygen you need to make life,” she said. “So the fact that it’s lower than some earlier, wishful-thinking estimates is not such a problem.”

Studying Europa’s atmosphere is “an important puzzle piece in learning about the moon as a system,” said Carl Schmidt, a planetary scientist at Boston University who was not involved in the work.

But the findings only confirm the amount of oxygen born in the ice. The study doesn’t reveal how much of the molecule gets lost to the atmosphere, or how it might permeate the ice to enrich the ocean below.

In other words, Dr. Schmidt said, “we still have no idea just how much is going down as opposed to going up.”

Juno won’t make any more close flybys of the global water world, but next-generation missions specifically intended to study Europa might find more answers. The European Space Agency’s Jupiter Icy Moons Explorer, expected to arrive at the Jovian system in 2031, aims to confirm the existence and size of Europa’s ocean. And NASA’s Europa Clipper, scheduled to launch in October, will investigate how the moon’s icy shell interacts with the water below.

For now, astronomers have their hands full with data from Juno. Though the flyby lasted only a few minutes, it was the first time the composition of plasma near Europa’s atmosphere was directly measured.

“This is just the tip of the iceberg,” Dr. Szalay said. “For many years, we’re going to be digging through just this one flyby to find all the treasure.”

By Thursday, Google will have changed how it displays certain search results. Microsoft will no longer have Windows customers use its Bing internet search tool by default. And Apple will give iPhone and iPad users access to rival app stores and payment systems for the first time.

The tech giants have been preparing ahead of a Wednesday deadline to comply with a new European Union law intended to increase competition in the digital economy. The law, called the Digital Markets Act, requires the biggest tech companies to overhaul how some of their products work so smaller rivals can gain more access to their users.

Those changes are some of the most visible shifts that Microsoft, Apple, Google, Meta and others are making in response to a wave of new regulations and laws around the world. In the United States, some of the tech behemoths have said they will abandon practices that are the subject of federal antitrust investigations. Apple, for one, is making it easier for Android users to interact with its iMessage product, a topic that the Justice Department has been investigating.

“This is a turning point,” said Margrethe Vestager, the European Commission executive vice president in Brussels, who spent much of the past decade battling with tech giants. “Self-regulation is over.”

For decades, Apple, Amazon, Google, Microsoft and Meta barreled forward with few rules and limits. As their power, riches and reach grew, a groundswell of regulatory activity, lawmaking and legal cases sprang up against them in Europe, the United States, China, India, Canada, South Korea and Australia. Now that global tipping point for reining in the largest tech companies has finally tipped.

The companies have been forced to alter the everyday technology they offer, including devices and features of their social media services, which have been especially noticeable to users in Europe. The firms are also making consequential shifts that are less visible, to their business models, deal making and data-sharing practices, for example.

The degree of change is evident at Apple. The Silicon Valley company once offered its App Store as a unified marketplace around the world, but it now has different rules for App Store developers in South Korea, the European Union and the United States because of new laws and court rulings. The company dropped the proprietary design of an iPhone charger because of another E.U. law, meaning future iPhones will have a charger that works with non-Apple devices.

On Monday, Apple was fined 1.8 billion euros, or $1.95 billion, by E.U. regulators for thwarting competition among music streaming rivals.

The modifications mean that people’s technology experiences will increasingly differ based on where they live. In Europe, Instagram, TikTok and Snapchat users under the age of 18 no longer see ads based on their personal data, the result of a 2022 law called the Digital Services Act. Elsewhere in the world, young people still see such ads on those platforms.

The tech industry is essentially maturing and becoming more like banking, automobiles and health care, with companies tailoring their products and services to local laws and regulations, said Greg Taylor, an Oxford University professor focused on competition in technology markets.

“This represents a sea change in how we regulate the tech sector,” he said. “Although the E.U. is the first out of the gate, other jurisdictions around the world are trying to do similar things.”

Yet even as the big tech firms make changes, smaller rivals like Spotify say much more government action is needed worldwide to seriously address their vast power. Many of the firms continue to report record profits and sales. Microsoft, Meta, Amazon, Apple and Alphabet, Google’s parent company, have helped push the stock market to new highs. Their combined market value has more than doubled since the end of 2019 to nearly $10.6 trillion.

Even policymakers behind some of the new rules said it was unrealistic to assume the new laws and regulations would immediately dislodge dominant companies like Google or Apple. Andreas Schwab, a member of the European Parliament who helped write the Digital Markets Act, said the hope was that over time, the rules, if strongly enforced, would provide space for new entrants to emerge and grow.

“The tipping point will be reached when we have more competition and not just a change of some products,” said Mr. Schwab, who traveled to Brazil, Japan, South Korea and Singapore over the past year to discuss the European Union’s new tech rules. “Maybe in one year we say they were important, or maybe in one year we say it’s a joke because the changes didn’t mean anything.”

Amazon, Apple, Google, Meta and Microsoft declined interview requests.

Few laws have forced the tech firms to make as many adjustments as the Digital Markets Act. The E.U. law was passed in 2022 to bar the biggest tech companies from using their interlocking services and deep pockets to box in users and squash rivals. The law affects everything from online advertising to messaging apps to app payment methods. Violators could face penalties of up to 20 percent of their global revenue.

For more than a year, tech companies have negotiated with E.U. regulators in Brussels about changes to their products, services and businesses to come into compliance.

In January, Google said it would reduce the visibility of its own services in search results and link more to rivals on queries for things like flights and restaurants. The company also pledged to let European users limit personal data from being shared across services like search, YouTube and Chrome — a shift long sought by privacy groups.

That month, Apple said it that in addition to the change allowing rival app stores and payment services, customers in Europe with a new iPhone would see a screen to select a default browser instead of the iPhone’s automatically defaulting to Apple’s browser, Safari.

Around the same time, the Digital Services Act, intended to combat illicit content online, has also begun having an effect. European users have gained new tools to report toxic content. Online platforms like Google and Meta can no longer allow advertisers to target users based on their ethnicity, political views and sexual orientation. TikTok and Instagram users can also choose to see posts without any recommended content chosen by an algorithm based on their personal data.

Europe’s aggressive approach is increasingly being emulated abroad. In Australia, a 2021 law required companies like Alphabet and Meta to pay the country’s media outlets for distributing news articles on its sites, leading to an estimated $100 million in deals. On Thursday, Meta said it would not renew the deals with Australian media companies, potentially leading to further government action.

In Indonesia, TikTok closed its online shopping service last year after the country banned e-commerce transactions on social media platforms. Nepal banned TikTok altogether last year. India banned the app in 2020.

In the United States, momentum is also building. The Federal Trade Commission sued Meta in 2020, arguing the company snuffed out nascent competition by buying young rivals. It sued Amazon last year over claims the company had squeezed small merchants on its site.

The Justice Department has also filed antitrust lawsuits against Google and could file one against Apple as soon as the first half of this year. The cases could result in orders for the companies to change their practices, or even a partial breakup of their businesses.

Some of the companies are making adjustments that get ahead of U.S. regulators. In June, Amazon pledged to allow merchants to sell via its Prime subscription program without using its own logistics network, announcing the change before the government complained that such practices were anticompetitive. Google is allowing more mobile payment options to app developers, instead of just its own, as part of a proposed deal with state attorneys general.

Legal fights loom. The Supreme Court heard arguments last month over whether Texas and Florida could legally bar sites like Facebook and TikTok from taking down certain political content. If the states prevail, it will upend how online platforms can set the terms of engaging on their sites without U.S. government interference.

Nu Wexler, a former employee in the Washington offices of Google, Meta and Twitter, which has been renamed X, said the tech firms were “making more concessions” and “are being more pragmatic.”

They just “aren’t as invincible as they were five years ago,” he said.

Daisuke Wakabayashi contributed reporting from Seoul.

As Democrats look to wrest control of the U.S. House of Representatives in November, their fight will fully begin with Tuesday’s primaries in California.

And their immediate trouble is not Republicans. It’s Democrats themselves.

In the Republican-held Central Valley district stretching from Bakersfield to Fresno, which would have favored President Biden by 13 percentage points in 2020, a battle between two Democrats has become so personal that some in the party fear they could divide the vote, leaving the incumbent, Representative David Valadao, competing in November against another Republican running to his right, Chris Mathys.

With so few truly contested seats to fight over this year, the prospect of an early lockout in California — where the top two finishers regardless of party affiliation compete in the general election — has brought out some heavy hitters, including Dolores Huerta, the 93-year-old labor and civil rights leader who co-founded the United Farm Workers with Cesar Chavez in 1962. She is suiting up again on behalf of former California Assemblyman Rudy Salas, the top choice of institutional Democrats. So is California’s governor, Gavin Newsom, who will rally voters for Mr. Salas on Sunday in an effort to box out the other Democratic candidate, State Senator Melissa Hurtado.

“I’m scared,” Ms. Huerta said on Thursday from the unassuming offices of her foundation, which is based in Bakersfield. “We need to do a lot more work.”

Control of Congress could be at stake. Of the 16 House districts won by Mr. Biden but currently in Republican hands, five are in California, making the state a linchpin of the party’s hopes of retaking the chamber, where Republicans currently hold a three-seat majority.

“It’s going to come down to these tossups, and Democrats would have to win around two-thirds of them to take the majority,” said Erin Covey, the House analyst at the nonpartisan Cook Political Report.

Only two of those 16 districts that Democrats are targeting — in the Tidewater region of Virginia and in Omaha — are in states with Republican governors.

The National Republican Congressional Committee, the campaign arm of House Republicans, calculated that two-thirds of the battle for control of the House will occur in states largely untouched by the presidential election. With no boost from the presidential organizing and get-out-the-vote efforts, N.R.C.C. officials have set up 24 field offices — the most ever — figuring they are on their own in defending the G.O.P.’s razor-thin majority.

Republicans have made it clear that they are eager to prosecute their case in blue territory. Conservatives have made gains in such states — especially in Southern California and in Long Island and other areas on the outskirts of New York City — by running on crime, the high cost of living and the influx of migrants. One major motivating issue for Democrats, abortion, has not had as much of an impact in states where voters see abortion rights as protected.

But Democrats will be playing on their home turf, with strong state-level organizations and weak Republican Party structures. And they insist that they are playing with a strong hand: the threat posed to abortion rights and other freedoms, including in Democratic states, by an all-Republican government with Mr. Trump at its helm. The possibility of a Trump White House and a Republican Senate could make the House a lone bulwark against complete G.O.P. control in Washington.

Democratic candidates say they understand they need to fight Republicans on issues like immigration. Will Rollins, a 39-year-old former federal prosecutor and Justice Department official running to flip the seat held by Representative Ken Calvert, Republican of California, said the G.O.P. had handed his party a “gift” when Republicans, at Mr. Trump’s behest, rejected a painstakingly negotiated bipartisan border security deal crafted in part by members of their own party.

“It is incumbent upon us to make these arguments and to run on issues that Republicans think they have the high ground: border, inflation and crime,” said Mr. Rollins, who ran in the same district, around Palm Springs, two years ago. He lost to Mr. Calvert, 70, by four points.

Mr. Calvert expressed confidence that nothing would change this time around. “Voters weren’t buying what Rollins was selling last time,” he said, “and they’re certainly not any more interested this time around in his radical, soft-on-crime policies.”

On the whole, Democrats start at a slight numerical disadvantage when it comes to taking back the House. Gerrymandering and the natural sorting of voters between dense urban areas that are heavily Democratic and vast rural districts that are strongly Republican have left vanishingly few in play.

The Center for Politics at the University of Virginia has rated just 10 Republican seats as tossups, nine of them in states with Democratic governors. Democrats hold only nine seats considered tossups, and only one in a state with a Republican governor.

Democrats would need five seats to win control of the House, and their prime California targets are the districts held by Mr. Valadao and Representatives John Duarte, Mike Garcia and Michelle Steel.

With so few opportunities, an unforced error taking Democrats out of play in Mr. Valadao’s district would loom large. In an interview, Mr. Salas did not discount the possibility, if Republicans come out in force to vote in a Super Tuesday presidential primary where Democrats appear to have less at stake.

“This could be a real scenario,” he said in an interview on Friday.

Ms. Hurtado was unapologetic in an interview last week over chile relleno at La Imperial Taqueria in Wasco, Calif., a town of 28,000 — if you count the prison population — surrounded at the moment by miles of blossoming almond trees.

“Obviously, I wasn’t the chosen one,” she said with a shrug. “But I like being the underdog.”

Democrats have improved their position in at least one California House race. Mr. Garcia’s district in northern Los Angeles County, redrawn in 2022, would have gone for Mr. Biden over Mr. Trump by more than 12 percentage points. Yet voters in the district nominated the same Democratic candidate, Christy Smith, three times against Mr. Garcia, and in every contest, Mr. Garcia beat her.

This time, Democrats have cleared the field for a new challenger, George Whitesides, a former NASA chief of staff and the former chief executive of the private space company Virgin Galactic. Mr. Whitesides has raised nearly $3.7 million, $271,000 of it his own money. Mr. Garcia has raised $3.2 million.

In an interview, Mr. Whitesides hit Mr. Garcia for selling as much as $50,000 in Boeing stock weeks before the House Committee on Transportation and Infrastructure released its highly critical investigation into the company’s 737 Max airliner, and talked up his own record in aerospace, in a district that relied on the industry.

“The fact that I’ve sort of created 700 jobs in the district helps a lot, too,” he said.

But infighting continues elsewhere. In a fierce fight for the Orange County seat vacated by Representative Katie Porter, a Democrat, State Senator Dave Min has been battling the political activist Joanna Weiss. Ms. Weiss has the backing of the pro-Israel United Democracy Project and Emily’s List, which works to elect female abortion-rights candidates. Those outside groups have pumped in more than $4 million against Mr. Min, Ms Covey said, and publicized charges of drunken driving while countercharges accuse her of racism. That will not make it any easier for Democrats to hold the seat.

That only makes the contest in Central Valley stand out more. When Democrats convinced Mr. Salas to run in 2022, he was considered a prized recruit, a popular state lawmaker who could have been the first Latino to represent the heavily Hispanic Central Valley.

That year, the drama was on the Republican side. Democrats tried to meddle in the so-called jungle primary by boosting Mr. Mathys, an ardent Trump supporter, in advertisements, hoping a hard-right candidate would be easier to beat than Mr. Valadao, who was one of just 10 Republicans to vote to impeach Mr. Trump for inciting the Jan. 6, 2021, attack on the Capitol. It didn’t work. Mr. Valadao beat Mr. Mathys by 1,220 votes for a distant second place behind Mr. Salas, and then stormed back to best the Democrat on Election Day by three points.

Democrats were ready to give Mr. Salas another chance this presidential election year, but Emily’s List convinced Ms. Hurtado to run as well, showing her data that indicated her vote totals in her State Senate races outpaced Mr. Salas’s votes in his House campaign.

Then Washington picked sides, fearing that Ms. Hurtado’s rise could leave Mr. Valadao and Mr. Mathys as the top two finishers on Tuesday.

House Majority PAC, the House Democratic leadership’s super PAC, is airing Spanish-language ads promoting Mr. Salas’s record on health care, while Mr. Salas, with the encouragement of Washington Democrats, has gone on air with an advertisement portraying Ms. Hurtado as hostile to abortion rights, for abstaining or missing votes on the issue in the State Senate. That was a painful expenditure for a candidate who has raised less than $747,000.

Ms. Hurtado, who has weathered more than $1 million worth of ads against her candidacy, has raised about a tenth of Mr. Salas’s total, $76,741. And Emily’s List does not include her as an endorsed candidate. But with the name recognition of a state senator whose district matches the U.S. House district by 95 percent, Democrats are sweating it out.

Ms. Hurtado is not, hoping that Mr. Salas’s negative ads will actually help her, especially with independents and Republican voters who have backed her in the past.

“If they were going to pick a side, they should have been upfront about it,” she said. “They could have said, ‘Step aside.’ They never did.”

Not since Theodore Roosevelt ran against William Howard Taft in 1912 have voters gotten the opportunity to weigh the records of two men who have done the job of president.

And despite holding intensely and similarly critical opinions both of President Biden and of his predecessor, Americans have much more positive views of Donald J. Trump’s policies than they do of Mr. Biden’s, according to New York Times/Siena College polls.

Overall, 40 percent of voters said Mr. Trump’s policies had helped them personally, compared with just 18 percent who say the same about Mr. Biden’s policies. Instead, 43 percent of voters said Mr. Biden’s policies had hurt them, nearly double the share who said the same about Mr. Trump’s policies, the latest Times/Siena poll found.

That presidents are frequently remembered more fondly once they leave office is nothing new. In a retrospective look at nine of the past 11 presidents, approval of job performance increased 12 percentage points after leaving office, both on average and for Mr. Trump in particular, according to a Gallup poll from June.

But recent Times/Siena polls highlight how comparatively well-regarded Mr. Trump’s policies are, even by groups that were affected by policies that Democrats hope will be motivating issues in 2024. And for many, it appears to be all about the economy.

Women are 20 percentage points more likely to say that Mr. Trump’s policies have helped them than Mr. Biden’s have, despite the fact that Mr. Trump installed Supreme Court justices who ultimately overturned the right to an abortion and that about two-thirds of women in America think that abortion should be legal in all or most instances.

Overall, the share of women who think Mr. Trump’s policies have helped them stands at 39 percent, with 26 percent saying his policies hurt them and 34 percent saying they didn’t make much of a difference.

In polls of six key battleground states in October, 42 percent of women said abortion should always be legal; among that group, two-thirds said Mr. Trump’s policies had hurt them. But women who thought abortion should be more limited — including those who said abortion should be mostly legal — were far more likely to say Mr. Trump’s policies helped them than hurt them.

“I like his policies,” said Nadeen Geller, 57, a homemaker who lives on Staten Island, N.Y., and plans to vote for Mr. Trump. “I think they work.”

“I think economically he can do wonders,” added Ms. Geller, who is in favor of keeping abortion legal before 15 weeks of pregnancy, and later for health reasons. “I just all around think he can do very well for this country.”

Views of the economy are deeply intertwined with views of the candidates’ policies. And while Republicans almost universally view the economy as bad, Democrats are more evenly split. Of the voters who said the economy was in excellent or good shape, large shares also said they had felt positive impacts of Mr. Biden’s policies. Democrats and Democratic-leaning independents who think the economy is fair or poor are more likely to say Mr. Biden’s policies have hurt them or haven’t made much of a difference.

Another of Mr. Trump’s early signature policies, his plan to build a wall on the U.S.-Mexico border, was opposed by two-thirds of Hispanic voters, according to exit polls taken during the 2016 election. It was part of a suite of policies, including a ban on travel from several predominantly Muslim countries, that helped fuel large turnout by Democratic voters and sweeping victories for Democratic candidates in the 2018 midterms.

Now, 37 percent of Hispanic voters said Mr. Trump’s policies helped them personally, compared with 15 percent who said this about Mr. Biden’s policies.

“Cash was flowing with Trump, even through the Covid years toward the end of his term,” said Henry Perez, 50, who lives in California’s Central Valley. He voted for Mr. Trump in 2016 but switched to Mr. Biden in 2020 because, as a union member, he was not thrilled with Mr. Trump’s policies toward unions.

Mr. Perez plans to vote for Mr. Trump again this fall, partly because of the economy.

“Just go to the pump and go to the store — that will tell you everything you need to know about how Biden’s policies have hurt me,” he said.

Black voters were the least likely to say Mr. Trump’s policies helped them, but they still viewed Mr. Trump’s policies more favorably than Mr. Biden’s.

Gameli Fenuku, a 22-year-old student in Richmond, Va., is planning to vote for Mr. Biden — mainly because “he said he was going to be making college more affordable for students.” But he said that Mr. Biden’s policies had hurt him overall, and that Mr. Trump’s had helped.

“I don’t want to say it was just because he was president, but everything was definitely cheaper,” Mr. Fenuku said of Mr. Trump, adding, “We weren’t just handing out money to other countries.” He said he would consider voting for Mr. Trump, an attitude that was once a rarity among young Black men like Mr. Fenuku but has become more prevalent in recent polls.

Mr. Biden’s student loan policies were also cited by Mary Turak, 64, a nurse living in Pittsburgh. Ms. Turak, a Democrat, said that the people around her were “more financially secure” under Mr. Biden, with new jobs, better pay and less student loan debt.

“One of my daughters got hers completely forgiven,” Ms. Turak said, adding, “I’ve still got another daughter with some student debt that looks like it’s probably going to get forgiven at some level.”

But overall, across gender, age, race and education, voters were more likely to say that Mr. Biden’s time in office had hurt more than helped.

“He’s not really taking care at home,” said Jonathan Jones, 35, of Plant City, Fla., citing the wars and the economy as reasons he disapproves of Mr. Biden’s policies.

Mr. Jones, who used to work in manufacturing and now takes care of his mother, voted for Mr. Biden in 2020 but plans to vote for Mr. Trump in 2024.

“Even though Donald Trump gets on my nerves sometimes with his comments, he really was helping the people,” Mr. Jones said. “Whether it was food, housing, gas, to jobs.”

For the candidates’ own supporters, views of their policies seem to match their enthusiasm gap. Half of Mr. Biden’s 2020 supporters said his policies have not made much of a difference for them either way. The vast majority of Mr. Trump’s 2020 supporters said that his policies had helped them.

In fact, among the small number of Mr. Biden’s 2020 supporters who said they planned to vote for Mr. Trump this fall, nearly 60 percent said Mr. Biden’s policies had hurt them. Only a handful said his policies had helped them.

Mr. Biden is, however, winning among the sizable groups of voters who say that either his policies or Mr. Trump’s have not made much of a difference.

And going back to that race in 1912, who did voters end up choosing? Neither Taft, the incumbent, nor Roosevelt, his predecessor and challenger. Woodrow Wilson defeated both of them.

President Biden’s advisers are eager for the coming general-election fight and counting on voters to start paying more attention to Donald J. Trump, with the president himself even proposing and dashing off videos to ridicule the things his Republican rival says.

Mr. Trump is relishing the chance to contrast himself with Mr. Biden, as he did along the Texas-Mexico border last week, and trusting that Mr. Biden has the tougher job: convincing voters that their views of how the country is doing are wrong.

With the former president expected to rack up big wins on Super Tuesday and Mr. Biden preparing to deliver his State of the Union address on Thursday, this week is expected to clarify the coming choice for an American public that in many ways remains in disbelief that 2024 is headed toward a 2020 rematch.

Both campaigns see the coming days as a critical period that will set the tone and define the early contours of the presidential campaign.

By most accounts, Mr. Biden begins behind.

A New York Times/Siena College survey over the weekend showed Mr. Trump ahead 48 percent to 43 percent among registered voters. Mr. Biden is hampered by widespread concerns about his age and his handling of the job, fractures in the Democratic coalition over Israel and a general sourness about the state of the nation.

But Mr. Biden also enters the expected general election contest with a number of key structural advantages, including a sizable financial edge and a lack of distractions on the scale of Mr. Trump’s four criminal trials.

Quentin Fulks, Mr. Biden’s principal deputy campaign manager, said the campaign had been preparing for a week that will functionally serve as “the kickoff to the general election.”

“The problem that we’ve been facing is that a number of people are telling us that they’re not aware that this is a choice between Joe Biden and Donald Trump,” Mr. Fulks said. “March is going to be our time to make that choice crystal clear.”

The month begins with Super Tuesday and is set to end with jury selection in Mr. Trump’s first criminal trial, in New York, for hush-money payments made secretly to a pornographic film star in the heat of the 2016 campaign. In between, Mr. Trump is expected to effectively clinch the nomination and complete a takeover that will give him operational control of the Republican National Committee.

“Whatever advantage they may have in timing, we will far surpass in the passion of our supporters and our ability to organize them,” said Chris LaCivita, one of two co-managers of the Trump campaign whom Mr. Trump plans to install as chief operating officer of the R.N.C. Polls show Mr. Trump so far better uniting his 2020 coalition than Mr. Biden. “They have a motivation problem,” Mr. LaCivita said. “We don’t.”

Mr. Trump, however, does have legal problems.

His team was elated last week when the U.S. Supreme Court laid out a timeline for hearing Mr. Trump’s claim of immunity from prosecution for his actions after his 2020 election loss to try to stay in power. The Supreme Court’s schedule pushes until late summer at the earliest Mr. Trump’s federal trial.

Nikki Haley is still running in the Republican primary but polls predict a wipeout on Super Tuesday, with 15 states in play. Mr. Trump’s team believes he could surpass a majority of delegates and secure the nomination as early as March 12. On Friday, the Republican National Committee is meeting in Texas and is expected to ratify Mr. Trump’s new pick to lead the party, Michael Whatley.

“We’re going to get 100 percent control of the mechanics we need,” Mr. LaCivita said.

The Biden team has long circled this Thursday’s State of the Union address as a pivot point, knowing it will be the president’s largest audience most likely until the summer convention and a chance both to sell a skeptical American public on his accomplishments and fill in a second-term agenda that has so far been scarce on details.

After the speech, Mr. Fulks said, the Biden campaign will unleash a “show of force,” with Mr. Biden’s first two stops already announced as events in Atlanta and Philadelphia.

Mr. Biden, Vice President Kamala Harris and the first lady, Jill Biden, are all expected to fan out on the campaign trail. One sign of the Biden campaign’s early organizing edge: It is planning, along with the party, to open 31 general election offices in the next 30 days in the key battleground of Wisconsin alone.

Mr. Trump has yet to announce any general election staff in the state.

The first lady’s Saturday appearance in downtown Tucson, Ariz., offered a warning sign of the protests likely to greet the administration’s leading figures on the trail. Her “Women for Biden” event was interrupted four times in 15 minutes by dozens of pro-Palestinian protesters who object to her husband’s support for Israel in the Israel-Hamas conflict.

The Biden team has stage-managed events to avoid such outbursts.

Mr. Trump arranged his own presidential-style photo op at the border at the same time as Mr. Biden’s official visit. Mr. Trump’s trip was announced days before Mr. Biden’s. In two Texas border cities, both men chatted with law enforcement officers, Mr. Biden indoors, Mr. Trump outside overlooking the Rio Grande — and Mr. Trump’s team pronounced itself pleased with the result.

“In an age where visuals matter, it’s probably a fight they won’t pick again,” Mr. LaCivita said.

But in a twist, many Democrats are now hoping for increased coverage of Mr. Trump. The current Biden team thinking is the more Trump the better, in order to remind voters about what they didn’t like about him in the first place. Some Biden officials welcomed national television networks carrying Super Tuesday’s results with special coverage because more voters would grapple with the reality of a Biden vs. Trump contest.

Mr. Trump’s advisers see a benefit to his time out of the limelight. The decision by social media platforms to banish him after the Jan. 6, 2021, riot has meant that his all-capital-letters screeds are now confined to his Truth Social website. That has kept some of his most raw and incendiary commentary confined to the conservative ecosystem, where only his supporters consume it.

To highlight some of Mr. Trump’s more inflammatory remarks, the Biden team has begun producing split-screen videos of the president watching them on an iPad and then delivering a pithy retort. The president is said to enjoy producing these videos, according to three people familiar with the matter. Mr. Biden himself had, on a recent fund-raising swing, pitched the specific video responding to Mr. Trump comparing himself to Aleksei Navalny, the Russian dissident who died in prison, two of the people said.

One concern that Mr. Trump’s allies have had for months is being out-raised — and therefore outspent — by the Biden campaign, the Democratic Party and allied groups.

The main super PAC aligned with Mr. Biden has already announced a $250 million television and digital ad reservation beginning in August. Mr. Trump’s super PAC had less than $20 million on hand entering February, and was refunding $5 million each month to an account paying Mr. Trump’s mammoth legal fees.

Taylor Budowich, the chief executive of the Trump super PAC, which is providing briefings to several of its top donors at Mar-a-Lago on Super Tuesday, said his group had the easier political task despite the financial disparity.

“He has the job of convincing people what they believe and feel isn’t true,” Mr. Budowich said of Mr. Biden and voter displeasure with the nation’s direction. “We have the job of convincing people that it is true — and the guy currently in charge is responsible for it.”

Mr. Trump will keep talking about the economy, immigration, energy and, as he puts it, the “weaponization of government” against him through four indictments.

Mr. Biden’s team sees abortion and Mr. Trump’s appointment of Supreme Court justices who overturned Roe v. Wade — and the recent Alabama court ruling on in vitro fertilization — as powerful messages. The president’s State of the Union speech is expected to feature an economic agenda that contrasts with Mr. Trump’s.

Mr. Trump’s team sees immigration as a particularly resonant issue to press with Black voters in large cities where there have been influxes of migrants from the southern border.

The super PAC supporting Mr. Trump will start running ads Monday on Black radio stations in Georgia, Michigan and Pennsylvania, emphasizing the migrant crisis and Mr. Biden’s support for transgender protections. Despite a lengthy history of racist statements, Mr. Trump is performing better in polls with Black voters than he has in his previous campaigns. The Biden campaign has been trying to shore up its support with Black voters with its own advertising.

Mr. Trump’s legal exposure is likely to dominate the news in the coming weeks, with his New York trial set to begin on March 25. Privately, several Trump allies marveled at the timing breaks he has had throughout the process. The Manhattan trial could be the only pre-election trial he faces.

The case, however, is expected to last six weeks, taking him off the campaign trail for days at a time. One person familiar with internal discussions, who was not authorized to speak publicly, said Mr. Trump would most likely campaign on weekends, and use Wednesdays — when the trial is expected to pause each week — for fund-raising or to meet with advisers.

No presidential candidate has ever campaigned under such circumstances.

Kellen Browning contributed reporting from Tucson, Ariz., and Michael Gold from Eagle Pass, Texas.

Kacey Poynter doesn’t have to commute far to clock in for work. She’s a paid caregiver and simply rolls out of bed to tend to her charge: her 2-year-old son, who sleeps in a portable playpen right beside her.

Sonny was born with a congenital malformation that impaired his brain development and needs near continuous care simply to breathe and eat. Ms. Poynter left her job at a call center when she brought him home from the hospital and has nursed him ever since rather than relying on aides or institutions. Indiana’s Medicaid program has paid her for this labor of love.

“It’s just been honestly life-changing, being able to be here with him and not worry about someone else trying to take care of him,” she said.

But her ability to keep looking after him is now in doubt. Indiana’s social services agency has announced plans to end the caregiver program, citing a nearly $1 billion shortfall in the state Medicaid budget. By July 1, parents and guardians caring for children and spouses caring for their partners would have to enroll in a different program for far less pay.

The fear, for people like Ms. Poynter, is that they will have no option but to return to work and search for home care help in the midst of a deepening national labor shortage of aides and nurses.

During the coronavirus pandemic, states received a huge infusion of federal money — money that’s now drying up, leaving Indiana, and many other states, facing tough choices about how to plug the gaping holes in their budgets.

Panicked Indiana parents who rely on the payments have held weekly rallies at the Statehouse, some toting their children. With the state legislative session ending as early as Friday, it’s unclear how the proposed cutbacks will play out.

Lawmakers point to hard budgetary math and the hazy line between above-and-beyond care that merits payment and the duties all parents owe their children.

“We have a lot of legislators who say, ‘Nobody should be depending on Medicaid to make a living,’” said Kim Dodson, chief executive officer of The Arc of Indiana, a nonprofit advocacy group. “But you have families who have made a choice to not work outside the home, to care for their loved one, because there’s nobody else who can do it and certainly can’t do it as well as them.”

Indiana’s lieutenant governor, Suzanne Crouch, a Republican who is running for governor, has called on the social services agency to postpone the cuts and demanded an outside audit of the agency’s finances. “We’re going to be judged by how we care about the most vulnerable among us,” she said in a statement.

About four million Americans with chronic illnesses or disabilities receive home and community-based services paid for by Medicaid, the government’s health insurance program for lower-income people. Most are adults, but a growing share are children with serious medical conditions who may require both skilled services and help with daily living tasks like bathing and dressing.

These services, which keep many people out of nursing homes or other institutions, may be provided by nurses or home health aides, but families have always been the backstop. In many states, relatives can be paid for providing some of that care, but Medicaid programs have typically been more restrictive about paying parents who — the thinking goes — are obligated to care for their children out of duty rather than for money.

During the pandemic, the Biden administration relaxed hurdles for parents and guardians to become paid caregivers. Congress increased federal support for Medicaid, in part so states could expand caregiving programs. According to a survey last summer by KFF, formerly known as the Kaiser Family Foundation, 37 states took advantage of the expansion to pay parents and guardians.

Kate McEvoy, executive director of the National Association of Medicaid Directors, said that the paid programs offered a way to meet family needs and to save states money that might otherwise be spent on expensive institutional care. “They want to be served in a home setting or in the community, and generally it is less costly for the Medicaid program,” she said.

Now that federal funding is shrinking, some states are downsizing programs and tightening eligibility while others are making paid caregiving permanent.

Virginia initially imposed stricter regulations for parents to become paid caregivers, but legislators are now considering a bill to lift some requirements. Ohio made its caregiving program permanent, but eligible parents or spouses must prove they cannot hire an aide, and paid hours are capped at 40 a week. Iowa and Oregon are asking the Centers for Medicare & Medicaid Services to create new paid programs.

Ms. Poynter has been paid $15 an hour for eight hours of daily personal care, plus health insurance and retirement benefits through a nursing provider, Healing Hands, which contracts with the state and oversees her work.

Sonny is a joyful child, just beginning to roll over and talk, but he is completely dependent on his parents. Each day Ms. Poynter slowly feeds him liquid meals through a tube in his stomach, suctions sputum from the breathing hole in his trachea and cleans and bandages the openings to his airway and abdomen, in addition to changing diapers and other baby routines.

On her phone, she clocks in and out for the hours she will be paid, but the distinction feels arbitrary to her because Sonny is no less dependent on her when she is off. Paradoxically, she is required to clock out before she administers medicine because Medicaid considers that skilled care and she is only contracted for personal services. “My brain is on work-mode pretty much 24/7,” she said.

Statewide, enrollment in the program and its costs skyrocketed. From March 2022 to February 2024, the number of children with disabilities or traumatic brain injuries who had paid caregivers grew sixfold to 1,629 from 262, according to Indiana’s social services agency. Fueling that growth were the costs associated with the nursing providers under contract to oversee the program. Some providers competed to recruit caregivers, advertising online and offering $1,500 or more as signing bonuses, and hundreds of dollars for referrals.

That contributed to soaring spending on caregiving for the pediatric population, to a projected $173 million this year from $2.5 million in 2021.

Melissa Keyes, executive director of Indiana Disability Rights, an independent agency, said the state had drastically underestimated the demand and failed to take steps like capping hours that some other states had imposed. “They didn’t necessarily have good guardrails in place for how that program should be managed,” she said.

The state approved nearly half of children’s caregivers for more than 60 hours per week, and a small share were approved to work around the clock.

Indiana didn’t flag the growing spending until the end of last year, when an updated forecast for Medicaid showed it was $984 million in the hole. Michele Holtkamp, an agency spokeswoman, said that the caregiving program was only one of several factors for the shortfall, “but it was the most acute.”

State Senator Ryan Mishler, a Republican who is the chairman of the Senate appropriations committee, said that in a few cases providers had billed the state more than $200,000 for the care of a single individual. “The whole point of home care is they say it’s less expensive. But when you get up to that much, it’s actually not.”

The state’s social services agency maintains that caregivers can enroll in a substitute Medicaid program that it says is just as good. But it pays less, with a maximum of about $34,000 a year. In the existing program, Ms. Poynter can make about $50,000 a year, and other caregivers approved for more than eight hours a day are paid substantially more.

State Representative Edward Clere, a Republican, blamed the agency’s limited release of details for the outcry. “It is scary for families to be told that there are going to be major changes but not have enough information to understand what those changes will mean for them,” he said.

Families in rural areas may be particularly hard-pressed to find help caring for their children. Indiana has 26 percent fewer home health aides than the national average, according to AARP.

Lydia Townsend, a service coordinator for Healing Hands who oversees more than 200 caregivers, including Ms. Poynter, said boundaries should be set to avoid any abuses of the system. But she worried that the proposed cuts would endanger families. “They’re not going to have a roof and food like what they’re able to have now,” she said.

The fallout this year from the federal government’s reduced Medicaid funding is rippling across many states at a time when their tax revenues are also falling. KFF projects that states’ expenditures on Medicaid will rise a startling 17 percent this year.

Alice Burns, associate director of KFF’s program on Medicaid and the Uninsured, asked what would be sacrificed if Indiana continued to spend so much on the caregiving program: “Wraparound services for pregnant women? Dental care for children? What are the services people will have to do without?”

Ms. Poynter isn’t sure what she will do if the cutbacks are approved, but ruled out turning to a stranger for help. She’ll probably care for Sonny until her husband gets off work and then pick up evening shifts as a waitress or a barista. Compared with friends who are sole caregivers, she said that she felt fortunate.

But nothing could make up for the time parents would have to spend away from their children, whose lives are precarious and often short.

“Tomorrow is not promised for them,” she said.

Canada’s emergency preparedness minister is warning that this year’s wildfire season will be worse than the record-breaking season of 2023, when thousands of fires burned tens of millions of acres and set off massive plumes of smoke that enveloped major U.S. cities, including New York and Washington.

This year’s fires could be especially bad in two of the country’s most fire-prone provinces, where nearly 150 of the blazes that started during last year’s season are still burning this winter, under snow-covered ground.

While so-called “zombie fires,” a term recently popularized in the Canadian media, are an annual phenomenon in parts of the country, never have so many fires been reported in a single winter, raising fears that many of them may flare up again above ground.

The “zombie fires” persist during winter because porous peat and moss ground cover in northern areas act as underground fuel for them.

The risk of wildfire in Canada has grown because of climate change, which increases the hot, dry and gusty conditions that have caused drought, according to research published last summer by World Weather Attribution, a group of scientists who model how climate change impacts extreme weather.

Given drought conditions in parts of Western Canada and other extreme weather effects, Harjit Sajjan, Canada’s emergency preparedness minister, said it was not surprising that the wildfire forecast was “alarming.”

He added that climate change “is the reality that we face and we need to get ready for it.”

Many of the underground fires — which are burning in the provinces of British Columbia and Alberta — don’t pose an increased risk of triggering wildfires in the spring because they are in places so charred that there is no vegetation left to burn.

But others are in areas that droughts have turned into tinder boxes, prompting fears that they will cause fires to erupt above ground once spring arrives.

Last year’s wildfires burned about 48 million acres of forest across Canada, an area roughly the size of Finland, and a staggering increase of 170 percent over the previous year, according to the Canadian Interagency Forest Fire Center.

Smoke from the fires, particularly blazes that burned in Quebec, wafted as far south as Florida and blanketed several cities in the United States and southern Canada in a noxious cloud.

The drought in Western Canada is now entering its third year and is a major factor behind fears of an even worse 2024 fire season, particularly in British Columbia and Alberta.

Both provinces have already seen new aboveground wildfires this year, prompting Alberta to declare a start to its wildfire season about a week before the traditional March 1 start date.

Snow could still fall in the spring and tame the existing fires and help with the dry conditions, said Mike Flannigan, a professor of wildfire science at Thompson Rivers University in Kamloops, British Columbia.

But this year, he added, long-range forecasts suggest continued dryness and warmer than usual temperatures.

About 93 fires left over from last year have continued to burn underground through the winter in British Columbia, while 55 are burning in Alberta, according to their provincial governments.

Such winter fires are common in both provinces, as well as in Yukon, but, in British Columbia, there are usually no more than about 15, experts said, adding that this year’s much higher tally has left them surprised and worried.

“There’s no historical analog to what we’re seeing right now,” Professor Flannigan said. “Most years they’re not a big deal. But now a lot of these fires have the potential that when the snow melts and it gets warm, dry and windy to actually grow again. So it is a serious issue.”

No overwinter fires have been recorded in the forests of Quebec, the eastern province that sent smoke billowing into the United States and at one point across the Atlantic Ocean to Europe. Quebec generally lacks the peat and moss soil of the western provinces that serve as fuel for winter fires.

Since the winter fires are underground and can produce little or no visible smoke, tracking them can be a challenge. The wildfire service for British Columbia said that it relied on sensors in airplanes and satellites to look for heat, though snow cover reduces their effectiveness.

Still, some fires have been visible to the naked eye.

“Even on the -40, -42 Celsius days, we were still seeing smoke,’’ said Sonja E.R. Leverkus, the senior fire lead at Northern Fire Worx, a private wildfire fighting service in a remote section of northeastern British Columbia. “So much that as you drove you’d be smelling the smoke and coughing in your truck.”

In a typical year, melting snow seeps into the ground where winter fires burn and snuffs most of them out. But this year there has been far less snow than usual, said Dr. Leverkus, who holds a doctorate in fire ecology.

“I am 6 foot 2, and there have been times in the past few years that snow on my apple orchard has been well above my hips,” she said, adding that there was less than foot on the ground.

Mr. Sajjan, the emergency preparedness minister, said that Canada was better prepared this year to fight fires and evacuate communities. While provinces and territories are responsible for fighting fires, federal money has provided for the training of an additional 600 firefighters across the country.

A system meant to allow provinces to share personnel and equipment has been revamped to make it more efficient and accelerate the exchange of information, Mr. Sajjan said.

Equipment stocks have been increased, he added, and new techniques and technologies — including nighttime firefighting — are being introduced or tested.

While the forecast for this year’s wildfire season seems dire, Professor Flannigan stressed that it was still only a prediction.

“I don’t expect to see another year like 2023 in my lifetime, but I could be wrong,” he said.

Still, he added, the long-term outlook for Canada was discouraging.

“Most every year is going to be a bad fire year,” Professor Flannigan said. “But on average, we’re going to see a lot more fire, a lot more smoke. This trend is going to continue.”

In Fort Nelson, British Columbia, Dr. Leverkus, whose crew numbers over 100 at the peak of fire season, said she was still haunted by the eight deaths among firefighters in Canada last year. Two of them occurred in areas near where her crews were working.

“Last year was horrible,” she said. “My crew and I, we listen to what the land is telling us. And the land is telling us that it’s dry, and the animals are telling us that it’s dry and to be ready.”

Vjosa Isai contributed research.