That mix of qualities is not easy to find.

“I think Trump has a problem in that he wants two different things,” said Lawrence H. Summers, who served as Treasury secretary in the Clinton administration. “He wants somebody who will be deeply loyal, and he wants someone who will be deeply reassuring to markets. Since markets are fearful of the tariff agenda, it’s hard to square both things.”

In recent days, Mr. Trump has been considering several candidates for the job, and their prospects have been rising and falling by the hour, according to people familiar with the deliberations.

The current front-runners are Scott Bessent, the billionaire hedge fund manager, and Kevin Warsh, a former Federal Reserve governor. Marc Rowan, the chief executive of Apollo Global Management, is also in the running, while Howard Lutnick, Mr. Trump’s transition co-chairman who is the chief executive of Cantor Fitzgerald, appears to have fallen out of favor.

Mr. Trump has made unorthodox choices for some cabinet posts. But a Treasury secretary pick that is seen as unserious could rattle markets and impede his ability to deliver on his economic promises. For that reason, Mr. Trump needs a secretary who is respected in corporate America while striking the balance of supporting tariffs without seeming to be a zealot who will tank the global economy by starting trade wars.

“Investors are on edge regarding the Trump Treasury secretary pick and what it might signal about the balance of power within the administration on economic policy, the mix of market-friendly versus -unfriendly policies, and how less market-friendly trade and immigration policies plus deficits will be calibrated to mitigate adverse impacts,” analysts at Evercore ISI wrote in a note to clients this week.

Analysts at the research group Beacon Policy Advisors theorized on Tuesday that Mr. Trump has the stock market in mind as he considers his decision. They noted that one reason Mr. Trump has not selected Robert Lighthizer, his trusted former trade representative and the architect of the tariffs in his first term, is because the president-elect is mindful of the effect that the choice will have on markets.

“Ultimately, Trump will likely select a nominee who can sell his tariffs to the markets rather than mitigate them,” they wrote in a report analyzing the stakes of the decision. “When it comes to Trump, tariffs can be seen as an end goal in themselves.”

Although the Treasury secretary does not direct trade policy or enact tariffs, the person in the role is generally the economic face of an administration whose goal is to instill confidence in the U.S. economy. The Treasury secretary is expected to explain America’s economic policies to companies and investors around the world, helping to ensure that investment flows into the United States and investors continue to see its debt as a solid investment.

Federal debt as a share of G.D.P.

The Treasury Department is at the core of the federal government and issues debt to fund the nation’s operations and pay its bills, including paying Social Security and veterans benefits. Although the American economy is the strongest in the world, the national debt is approaching $36 trillion, and prices remain high after two years with record levels of inflation.

“Whoever becomes Treasury secretary will face a full plate and daunting challenges, including making the case for large tax cuts, which will cause a huge explosion in debt and deficits, dealing with the Fed — and perhaps combatively so — on behalf of the president,” said Mark Sobel, a longtime former Treasury official.

He added that Mr. Trump’s Treasury secretary will also have to deal with “jousting over the dollar and exchange rate policy with noisy White House and trade teams calling for devaluation.”

Mr. Trump has often said that, for the sake of U.S. exports, he would prefer to see the dollar weaken because that would make American goods cheaper to buy overseas. But most economists expect his plans to impose tariffs on imports and cut taxes, among other actions, to do the opposite.

The day after the election, the dollar rose the most it had in years against a basket of other major currencies. And it has continued to rise, hitting a fresh high for the year last week.

Mr. Trump’s victory also has led to unease among bond investors, who worry about government largess and the resurgence of inflation under the president-elect. That has led to a rise in bond yields, which means investors expect to be paid more in interest in exchange for lending to the government.

A booming stock market is another priority for Mr. Trump, who sees stock prices as a critical indicator for the health of the economy. However, during Mr. Trump’s first term, each new round of tariffs that he imposed on Chinese imports sent stocks falling.

That dynamic is likely to play out again, as Mr. Trump has called for blanket tariffs as high as 50 percent on imports and even higher tariffs on goods from certain countries.

“Tariffs are going to increase costs on a lot of U.S. multinationals” said Brad Setser, a senior fellow at the Council on Foreign Relations. “The conventional wisdom is that would make many in the market nervous.”

Mr. Setser, who served as the deputy assistant secretary for international economic analysis at the Treasury Department from 2011 to 2015, said the desire for a rising stock market and higher tariffs are “somewhat in tension” and that Mr. Trump’s Treasury secretary will have to grapple with those crosscurrents.

As Mr. Trump and his advisers have been considering that pick, a belief in the merits of tariffs has been a priority. Mr. Trump’s first Treasury secretary, Steven T. Mnuchin, often argued against increasing tariffs on China and warned about the potential market implications.

That has put the views of the current group of front-runners in focus.

Mr. Warsh argued in a 2011 Wall Street Journal essay written with Jeb Bush, the former Florida governor who ran against Mr. Trump in 2016, that “we must find our voice to resist the rising tide of economic protectionism.”

Mr. Bessent has suggested recently that Mr. Trump’s tariff threats are a “maximalist” negotiating strategy to secure better free trade deals, and he has expressed concern about flouting World Trade Organization rules. Those comments led some of Mr. Bessent’s detractors to argue that he is not a true believer in tariffs or, as the increasingly influential billionaire Elon Musk recently said, “a business-as-usual choice.”

“Business-as-usual is driving America bankrupt, so we need change one way or another,” Mr. Musk, who expressed support for Mr. Lutnick to get the job, wrote on social media on Saturday.

For Mr. Trump, the decision could ultimately come down to whom he most trusts to be loyal.

Stephen Moore, a Heritage Foundation economist who advised Mr. Trump’s first campaign, said that Mr. Trump benefits from aides who will try to steer him away from making mistakes but that he has learned to prioritize hiring people who believe in his policies. That is especially true, he said, when it comes to tariffs.

“If you’re going to go in and work for Trump, you’ve got to be onboard with the agenda,” Mr. Moore said.

In a statement announcing his choice, Mr. Trump praised Mr. Duffy as a “tremendous and well-liked public servant” with the experience needed to lead the department, which has an annual budget of more than $100 billion and a vast work force.

“Sean will use his experience and the relationships he has built over many years in Congress to rebuild our nation’s infrastructure and usher in a golden age of travel,” Mr. Trump said in a statement.

Mr. Duffy served in Congress from 2011 to 2019 as a Republican. He resigned in September 2019 to help care for a newborn daughter with a birth defect, according to The Milwaukee Journal Sentinel.

Mr. Duffy departed Fox News Media on Monday, according to a spokeswoman for the network. He had joined as a contributor in 2020, offering political analysis across all Fox News Media platforms, and had hosted “The Bottom Line” on Fox Business with Dagen McDowell since 2023. He is not Mr. Trump’s only cabinet choice to come from Fox: Pete Hegseth, his pick for defense secretary, is a host on “Fox & Friends.”

Mr. Duffy originally rose to fame in the late 1990s on the MTV reality show “The Real World: Boston.” He also appeared on its sister show, “Road Rules: All Stars,” where he met his wife, Rachel Campos-Duffy, who is now a Fox News host herself.

If confirmed, Mr. Duffy will oversee a Federal Aviation Administration struggling with air traffic control and a Federal Railroad Administration still pushing for safety reforms after a fiery derailment in East Palestine, Ohio, in 2023. He will also be in charge of assessing how to rebuild the country’s crumbling infrastructure.

Mr. Duffy would also be managing remaining funds from the 2021 $1 trillion infrastructure law, a cornerstone of the Biden administration’s efforts to prioritize rebuilding the nation’s infrastructure, and would help to shape its priorities.

Mr. Duffy’s nomination did not appear to set off the sort of opposition that some of Mr. Trump’s other cabinet picks have.

“Transportation policy has a long bipartisan history,” said Representative Rick Larsen of Washington, the top Democrat on the House Transportation Committee, “and I look forward to continuing to maintain the tradition under former Representative Sean Duffy’s leadership and working together to pass the next surface transportation authorization, creating more jobs, if he is confirmed.”

Airlines for America, which represents the country’s largest airlines, praised Mr. Duffy’s nomination. In a statement, Nicholas E. Calio, the president and chief executive of the trade group, said, “Congressman Duffy has a proven track record for getting things done, and we are eager to collaborate with him on key issues impacting the U.S. airline industry.”

A Wisconsin native, Mr. Duffy began his political career as a district attorney for Ashland County, in the northern part of the state. He resigned after winning his congressional election. During his time in Congress, Mr. Duffy served on the House Financial Services Committee.

Mr. Trump credited Mr. Duffy with clearing “extensive Legislative hurdles to build the largest road and bridge project in Minnesota History.” Mr. Duffy was a co-sponsor of bipartisan legislation, led by Senator Amy Klobuchar, Democrat of Minnesota, to support the St. Croix River bridge project, which connects Wisconsin and Minnesota.

As a Fox News contributor, Mr. Duffy was critical of Transportation Secretary Pete Buttigieg. On the “Tucker Carlson Tonight” program in December 2022, Mr. Duffy said the holiday airline travel chaos at the time had been foreseeable, adding: “What’s striking is how often this happens. There’s a crisis, and Pete Buttigieg decides to ignore it.”

Before his stint at Fox, Mr. Duffy joined CNN in 2019 as a political commentator. He provoked pushback from his on-air colleagues by embracing Mr. Trump’s position on immigration and promoting a debunked conspiracy theory about the special counsel investigation of Russian election interference.

A correction was made on

Nov. 18, 2024

:

An earlier version of this article misidentified the location of a major train derailment. It was in East Palestine, Ohio, not East Palestine, Pa.

When we learn of a mistake, we acknowledge it with a correction. If you spot an error, please let us know at nytnews@nytimes.com.Learn more

Mr. Trump’s choice to lead health and human services has made baseless claims about vaccines. His selection for defense secretary is a former Fox News host whose leadership experience has been questioned. His nominee for the director of national intelligence is a favorite of Russian state media.

“Donald Trump is a blunt-force instrument applying blunt-force trauma to the system,” said Stephen K. Bannon, Mr. Trump’s former chief strategist who remains close to him and was recently released from federal prison for defying a subpoena in the congressional investigation into the Jan. 6, 2021, attack on the Capitol.

Presidents do not normally approach cabinet selections this way. Historically, they work with their teams to figure out in advance what the system will tolerate, eliminating the possibility that skeletons in the closet of a nominee might emerge during Senate hearings.

Mr. Trump largely followed this risk-averse approach at the start of his first term. He appointed people like the four-star general Jim Mattis, who was confirmed with a 98-to-1 bipartisan vote to be Mr. Trump’s first defense secretary.

But this time, emboldened by victory and the submission of the Republican Party, Mr. Trump is innovating. He is using an approach that has been discussed in the past for judicial nominees, which is nominating so many extreme choices that they cannot all be blocked. The strategy has never been used for cabinet picks.

It is possible that enough Republican senators are willing to risk their careers to oppose Mr. Gaetz, although it is unclear what the backup plan would be should Mr. Gaetz falter. Mr. Trump’s personal lawyer and pick for deputy attorney general, Todd Blanche, is seen as a possibility.

It is also possible that Mr. Gaetz is confirmed, along with the three other nominees who have raised such a furor in Washington. Mr. Trump has wasted no time in barreling ahead and putting personal pressure on senators.

One thing is certain: His four choices would have had virtually no chance of confirmation in a Republican-held Senate in the Washington that existed before 2024.

The president-elect’s choice to lead the Defense Department, Pete Hegseth, is facing an allegation that he sexually assaulted a woman, which he has denied. Beyond that, Mr. Hegseth, a veteran of the wars in Iraq and Afghanistan, has faced questions about having the requisite experience to run a department with an $850 billion annual budget, three million employees and 750 military bases around the world.

Mr. Trump’s choice to run the Department of Health and Human Services, Robert F. Kennedy Jr., is not only a vaccine skeptic but also a supporter of abortion rights who has all but declared war on the pharmaceutical and food industries that have long funded the Republican Party.

And his choice for intelligence director, Tulsi Gabbard, has blamed the United States and NATO for provoking Vladimir V. Putin’s invasion of Ukraine.

Then there is Mr. Gaetz, who helped orchestrate the ouster of the previous Republican House speaker, Kevin McCarthy. Mr. Gaetz has been under a yearslong investigation by the House Ethics Committee into allegations that he engaged in sexual misconduct and illicit drug use.

Hours after Mr. Trump announced his selection as attorney general, Mr. Gaetz resigned from his seat as a House member from Florida, which effectively ended the investigation. But there is building pressure on the Ethics Committee to release a report on the inquiry.

The question has repeatedly come up in Washington about the vetting done for Mr. Trump’s nominees. The question misses the point. Little more than a cursory Google search would have shown that Mr. Gaetz, Ms. Gabbard and Mr. Kennedy would draw all kinds of protests. Mr. Trump nominated them anyway.

The Trump team, people briefed on its activities say, did engage in vetting for some of his choices, such as Mr. Hegseth. But the sexual assault allegation did not show up because it involved a private settlement agreement with the woman in question, the people briefed on it said.

That left the team dealing with the one thing that Mr. Trump tends not to like: information that he was unaware of, which became an unwanted headline in the media. Still, he has told aides he is firmly behind Mr. Hegseth.

Karoline Leavitt, the incoming White House press secretary, said Mr. Trump had won with “a resounding mandate from the American people to change the status quo in Washington.” She said he had picked “brilliant and highly respected outsiders to serve in his administration, and he will continue to stand behind them as they fight against all those who seek to derail the MAGA agenda.”

For much of the past decade, Mr. Trump has repeatedly swamped the system with provocations. Mr. Bannon memorably stated that their strategy for dealing with the news media was to “flood the zone” with manure.

The strategy has ensured that little focus stays on any single scandal. The caravan moves quickly on to the next, and the next, creating an overall blurring and flattening effect. He has survived them all, including 34 felony convictions and being held liable for sexual abuse.

He has already driven into retirement or primary defeat most of the congressional Republicans who opposed him in his first term. And since defeating Vice President Kamala Harris and becoming the first Republican to claim the popular vote since 2004, Mr. Trump has made clear he will tolerate little dissent from the G.O.P. majorities in the House and the Senate.

He has demanded that the next Senate majority leader, John Thune, allow recess appointments that would let Mr. Trump push through appointees who would otherwise be deemed unfit, making such an agreement a condition for anyone who wanted to be leader.

Liam Donovan, a former National Republican Senatorial Committee aide, said that “we’re on a collision course between traditional senatorial prerogatives and the unique power dynamics of the Trump restoration.”

Now, as Mr. Trump prepares to take office for the second time, he is demonstrating how confident he is that the branches of government will bend even further to accommodate him.

He plans to test just how far he can go.

She has since suggested that the United States covertly worked with Ukraine on dangerous biological pathogens and was culpable for the bombing of the Nord Stream gas pipeline from Russia to Germany in September 2022. European prosecutors and U.S. officials say that sabotage was carried out by Ukrainian operatives.

Ms. Gabbard’s comments have earned her sharp rebukes from officials across the political spectrum in Washington, who have accused her of parroting the anti-American propaganda of the country’s adversaries. Her remarks have also made her a darling of the Kremlin’s vast state media apparatus — and, more recently, of President-elect Donald J. Trump, who last week picked her to oversee the nation’s 18 intelligence agencies and departments.

Her selection to be the director of national intelligence has raised alarms among national security officials, not only because of her lack of experience in intelligence but also because she has embraced a worldview that mirrors disinformation straight out of the Kremlin’s playbook.

No evidence has emerged that she has ever collaborated in any way with Russia’s intelligence agencies. Instead, according to analysts and former officials, Ms. Gabbard seems to simply share the Kremlin’s geopolitical views, especially when it comes to the exercise of American military power.

In Russia, the reaction to her potential appointment has been gleeful, even if Mr. Putin’s government remains wary of American policies, even under a second Trump administration.

“The C.I.A. and the F.B.I. are trembling,” Komsomolskaya Pravda, a Russian newspaper, wrote on Friday in a glowing profile of Ms. Gabbard, noting, positively, that Ukrainians consider her “an agent of the Russian state.” Rossiya-1, a state television channel, called her a Russian “comrade” in Mr. Trump’s emerging cabinet.

Russian media has emphasized Ms. Gabbard’s desire to improve relations with Moscow, according to FilterLabs, a firm that analyzes social media, state-run news organizations and other internet postings to track public sentiment in Russia.

“Gabbard fits an overall pattern of Trump breaking with much of the post-Cold War consensus,” said Jonathan Teubner, the chief executive of FilterLabs. “She is, for Russia, the one that perhaps most perfectly embodies the changes they were hoping for from the U.S.”

Mr. Trump’s critics called the choice a dangerous one that would undermine national security and that signaled a deference to Mr. Putin’s worldview.

“Nominating Gabbard for director of national intelligence is the way to Putin’s heart, and it tells the world that America under Trump will be the Kremlin’s ally rather than an adversary,” Ruth Ben-Ghiat, a professor of history at New York University and the author of “Strongmen,” a 2020 book about authoritarian leaders, wrote on Friday. “And so we would have a national security official who would potentially compromise our national security.”

Asked for comment on Ms. Gabbard’s pro-Russia stances and her amplification of Moscow’s messaging, Trump transition officials sent a copy of the president-elect’s comments when he announced his pick: “I know Tulsi will bring the fearless spirit that has defined her illustrious career to our intelligence community.”

If confirmed, she would have responsibility to oversee the very agency that monitored and called out Russian disinformation and influence efforts throughout the 2024 campaign.

She faces an uphill battle for confirmation in the Senate.

Among members from both parties, her tacit support of Russia’s war aims in Ukraine and her repetition of Kremlin disinformation have raised doubts about whether she should be given oversight of the intelligence agencies, including the responsibility of preparing the highly classified daily intelligence briefings for the returning president.

In choosing her, Mr. Trump signaled his deep distrust of those agencies. During his first administration, he publicly rebuked senior intelligence officers when their assessments differed from his own. Ms. Gabbard’s iconoclastic views over the years suggest that she shares that distrust, especially when it comes to Russia and the war in Ukraine.

In several public appearances and in social media posts, she has outlined a policy not different from the views of Vice President-elect JD Vance, who has also emerged as a critic of American support for Ukraine.

If confirmed, Ms. Gabbard would not be the only voice on intelligence matters. John Ratcliffe, Mr. Trump’s final director of national intelligence in his first administration, has been chosen to be C.I.A. director. Ms. Gabbard would, however, still be influential in determining what intelligence Mr. Trump and other top officials see in the daily intelligence briefing, and would be in a position to highlight intelligence that reinforces Mr. Trump’s views.

For Ms. Gabbard, the invitation to join Mr. Trump’s administration represents a stunning political evolution. Only four years ago, she sought the Democratic presidential nomination, albeit as an anti-establishment candidate, and endorsed President Biden when he won the nod.

Since then, however, she has broken with the Democratic Party and drifted toward a conspiratorial view of the world and American power in it.

“This war and suffering could have easily been avoided if Biden Admin/NATO had simply acknowledged Russia’s legitimate security concerns regarding Ukraine’s becoming a member of NATO, which would mean US/NATO forces right on Russia’s border,” she wrote on Twitter, now known as X, when the war began in February 2022.

A month later, she posted a video on the platform saying the United States was operating 25 to 30 biological research labs in Ukraine. She accused the Biden administration of covering them up and said they could release dangerous pathogens, though she stopped short of claiming the labs were making biological weapons, as Russia has falsely claimed.

Ms. Gabbard’s remarks were quickly called out by Republican members of Congress, including Representative Adam Kinzinger of Illinois and Senator Mitt Romney of Utah.

Her willingness to criticize the Biden administration has made her, like other prominent critics of the government, a favorite source of anti-American content on Russia’s state television networks.

Vladimir Solovyov, a popular talk show host, called her “our girlfriend” in a segment in 2022. The program included an interview Ms. Gabbard did with Tucker Carlson in which she claimed that Mr. Biden’s goal was to end Mr. Putin’s control of the Russian government, according to Julia Davis, the creator of the Russian Media Monitor, which tracks Kremlin propaganda.

In fact, Ms. Gabbard honed her pro-Russia views on Mr. Carlson’s show on Fox News before his program was canceled. She became a regular guest and occasionally filled in as host when Mr. Carlson was away.

Clips from her appearances on Mr. Carlson’s show that repeated Kremlin talking points were quickly picked up by Russian state media.

In some cases, she echoed story lines that Russia’s propagandists created, which the Russians then recycled on their own media as evidence that the conspiracy theories they had manufactured were true. For the Kremlin, it was a virtuous cycle.

The frequency of her citations on Russian state television prompted sharp criticism and attention inside the U.S. government. Hillary Clinton, the former first lady, secretary of state and Democratic presidential nominee in 2016, once called her a “Russian asset.”

Ms. Gabbard, 43, has an eclectic political background, often occupying a space where the left and right overlap — such as in their opposition to foreign military intervention and a more sympathetic view of Russia.

She began in state politics in Hawaii at 21 and emerged as a talented, charismatic young Democrat, though one who often espoused the culture-war views of today’s right, taking early positions against abortion and same-sex marriage, for instance.

At the time, she was closely aligned with her father, Mike Gabbard, a leader of Hawaii’s movement against same-sex marriage. At one point, she inveighed against “homosexual activists” who were, she said, forcing “their values down the throats of the children in our schools.” (The statement came during her mother’s run for the state school board in 2000.) By the time she ran for Congress in 2012, she had expressed support for abortion rights and for same-sex marriage, later stating in a video apology that her earlier views on gay issues had been shaped by her father.

In 2003, she joined the Hawaii Army National Guard and served in Iraq in 2004 and 2005 as a specialist with a medical unit of the 29th Infantry Brigade Combat Team. After attending officer training in Alabama, she served a second tour in the region as a military police officer in Kuwait. She left the guard in 2020 to join the Army Reserve, where she continues to serve with the rank of lieutenant colonel.

In interviews, she has cited her military service as a factor in her political views about the exercise of American military might.

In 2013, she opposed President Barack Obama’s ultimately aborted plans for airstrikes against Syria. She later criticized the administration for failing to properly call out “Islamist extremists.” She also questioned evidence showing that Syrian forces used chemical weapons in an attack that killed dozens.

In 2016 she opposed the favorite for the Democrats’ presidential nomination, Mrs. Clinton, becoming an ardent supporter of her chief Democratic rival that year, Senator Bernie Sanders of Vermont.

Her willingness to challenge the Democratic establishment earned her an invitation to visit Mr. Trump at Trump Tower during the 2016 presidential transition period.

It also made her an appealing figure for conservative news bookers, particularly those for Mr. Carlson’s Fox News show. On one show, the two agreed that U.S. support for Syrian rebels seeking to topple Mr. Assad was aiding terrorists — an interview that came as Russia bombed U.S.-backed rebels in the name of combating terrorism.

Ms. Gabbard ultimately became a paid Fox News contributor (Fox says it ended her contract after she joined Mr. Trump’s transition team in August), as Mr. Carlson was emerging as an ardently anti-interventionist, and increasingly pro-Putin, figure in the MAGA movement.

As Russian forces gathered before their invasion of Ukraine in February 2022, Ms. Gabbard joined Mr. Carlson to speak out against Mr. Biden’s move to impose new sanctions against Russia, even as she said she opposed Russia’s military operation. “The reality is that these sanctions don’t work whether they were put in before or now or later,” she said. “What we do know is that they will increase suffering and hardship for the American people, and this is the whole problem with the Biden administration.”

Her appearances were regularly picked up by Russia’s state media, including the international network RT, which promoted her critiques and lauded her with headlines such as “Tulsi Gabbard dares to challenge Washington’s war machine” and “Biden wants regime change in Russia — ex-congresswoman.”

By this year, Ms. Gabbard’s politics converged with Mr. Trump’s. In October, she joined the Republican Party and hit the campaign trail on his behalf, extolling him as a peacemaker.

“A vote for Donald Trump is a vote for a man who wants to end wars, not start them,” she said at Mr. Trump’s rally at Madison Square Garden shortly before Election Day, “and who has demonstrated already that he has the courage and strength to stand up and fight for peace.”

Here’s why the issue has surfaced and what the law says:

What is Trump saying about a third term?

Mr. Trump has occasionally sent mixed and cryptic messages about how long he could stay in office.

While talking to House Republicans recently about clinching the White House and both chambers of Congress, Mr. Trump jokingly hinted that they could help prolong his presidency.

“I suspect I won’t be running again unless you say, ‘He’s so good we’ve got to figure something else out,’” Mr. Trump said.

In July, at a gathering of religious conservatives, he told Christians that if they voted him into office in November, they would never need to vote again. “Christians, get out and vote. Just this time,” he said. “You won’t have to do it anymore, you know what? Four more years, it’ll be fixed, it’ll be fine, you won’t have to vote anymore, my beautiful Christians.”

Speaking to members of the National Rifle Association in May, he said: “I don’t know, are we going to be considered three-term or two-term? Are we three-term or two-term if we win?”

And during his first term in office, Mr. Trump suggested to his supporters at a September 2020 rally in Nevada that term limits were not set in stone.

“We’re going to win four more years in the White House,” he said. “And then after that, we’ll negotiate, right? Because we’re probably — based on the way we were treated — we are probably entitled to another four after that.”

Yet when Mr. Trump was asked by a New York Times reporter on Election Day whether the 2024 campaign was his last, he said, “I would think so.”

How presidential term limits came about

The 22nd Amendment to the Constitution, which was ratified in 1951, says that “no person shall be elected to the office of the President more than twice.”

Kimberly Wehle, who teaches constitutional law at the University of Baltimore and wrote a book titled “How to Read the Constitution — and Why,” said that the measure left no ambiguity and was intended to place a check on the president.

“There was a concern about entrenching power in a kinglike manner,” she said.

Can Trump get around the 22nd Amendment?

Mr. Trump has effectively demonstrated an ability to bend the Constitution, Ms. Wehle noted, especially having appointed three of the justices who belong to the Supreme Court’s conservative majority. She pointed to the court’s ruling in July that Mr. Trump was entitled to substantial immunity from prosecution on charges of trying to overturn the last election.

“Trump managed to move the Constitution by doing things no one thought was possible, and then there’s no consequences for what he did,” she said.

But amending the Constitution to get around the two-term limit would be a very tall order.

Two-thirds majorities in both the House and Senate are required just to propose an amendment, far more than the slender majorities Republicans hold in both houses now, or two-thirds of the states have to call for a constitutional convention.

Ratifying an amendment is even more onerous: Three-fourths of all state legislatures — or of those state-level constitutional conventions — must approve it.

Serious, or a joke?

Representative Dan Goldman, Democrat of New York, isn’t treating Mr. Trump’s recent quip as a laughing matter.

Soon after Mr. Trump remarked that House Republicans could help pave his way to a third term, Mr. Goldman said he would introduce a resolution to reaffirm that the 22nd Amendment applies for presidents who serve nonconsecutive terms. The measure has little chance of advancing to the House floor for a vote with the chamber under Republican control.

“How he operates is by floating trial balloons that he often claims are jokes, but he’s very serious about it,” Mr. Goldman, who was lead counsel during Mr. Trump’s first impeachment in the House, said on Bloomberg TV. “And he’s been talking about staying on past this next term for years.”

Representatives for Mr. Trump’s White House transition team did not immediately respond to a request for comment.

Has a president ever served more than two terms?

Yes. President Franklin D. Roosevelt was elected to four terms, serving from 1933 to 1945, during the Great Depression and World War II. He died while in office. There was no 22nd Amendment then, but Roosevelt’s grip on power became a driving force for setting term limits for presidents.

“Four terms, or sixteen years, is the most dangerous threat to our freedom ever proposed,” Thomas E. Dewey said in 1944. He served as New York governor and lost to Roosevelt in 1944 and to Harry S. Truman in 1948.

Michael Gold and Annie Karni contributed reporting.