An Ivy League university. Distinguished law firms with Fortune 500 clients. The highest levels of government in the nation’s largest city.

As President Trump seeks to extract concessions from elite institutions and punish his perceived enemies, some of New York’s most powerful people are suddenly confronting excruciating decisions.

The hard choices they face seem almost to be pulled from the pages of a college ethics textbook: Fight back and put your institution and even your livelihood in jeopardy? Or yield and risk compromising foundational values and ideals?

Some have sued, or walked away from their jobs. Others have cut deals with the Trump administration, and faced ferocious criticism for what many see as capitulation.

Mr. Trump has sought financial agreements, fealty pledges and other concessions from all across the United States, and even from other countries. But his former hometown, New York City, is a prime target: It is a capital of industrial and cultural institutions — and of the elite liberal establishment that his presidency pits itself against.

The deal-cutting has come as a shock to some leaders.

“I have been surprised at the rush at times to assuage the White House from activity that has gone on from people who I just thought would display more courage,” said David Paterson, a former Democratic governor of New York.

But the choices can be agonizing.

“It becomes a challenge for them to speak out against something they know is wrong,” said Chris Dietrich, chair of the history department at Fordham University. “If they stick their head above the parapet, they feel they could be putting a number of other people at risk.”

He compared the current moment to the McCarthy era, when many stayed silent as Joseph McCarthy, the Red-baiting senator falsely accused citizens of being Communists.

‘Pillars of America’

Last week, sold-out Broadway crowds were leaping to their feet to cheer the actor George Clooney after his rousing performance as Edward R. Murrow, the 1950s-era broadcast journalist. Mr. Murrow famously stood up to Mr. McCarthy.

Just a couple blocks away in Midtown, Brad Karp, the chairman of the top-tier law firm Paul Weiss, was writing a memo to his employees explaining why he had reached a deal with Mr. Trump to do $40 million in pro bono work for causes the White House supports.

Mr. Trump, in an executive order, had threatened to suspend the law firm’s security clearances and bar its lawyers from federal buildings, which would have severely restricted its ability to represent clients in some cases involving the federal government.

Three other elite law firms Mr. Trump threatened — Jenner & Block, WilmerHale and Perkins Coie — have fought back by suing the administration. But Mr. Karp argued that in being targeted by Mr. Trump for its ties to the president’s political and legal enemies, the firm faced an “unprecedented threat” and an “existential crisis.” He wrote that he had learned “other firms were seeking to exploit our vulnerabilities by aggressively soliciting our clients and recruiting our attorneys.”

On Friday, another top New York law firm, Skadden, Arps, Slate, Meagher & Flom, agreed to provide $100 million in pro bono work on issues Mr. Trump supports in an effort to avoid its own punishing executive order.

Earlier this month, Rachel Cohen, a Skadden associate, submitted her notice of resignation after putting together an open letter that was signed anonymously by others from numerous firms in hopes of pressuring their own employers to speak out.

And in response to the actions at Paul Weiss, about 140 alumni of the law firm signed a letter to its chairman, calling the decision to settle “cowardly.”

“It is a permanent stain on the face of a great firm that sought to gain a profit by forfeiting its soul,” the lawyers wrote in the letter.

The firms’ willingness to make deals followed a move by Columbia University, which in the face of being threatened with losing $400 million in federal funding, announced plans to overhaul its protest policies and security practices and make other changes in line with the Trump administration’s demands.

On Friday, a week after the plans were announced, the university’s interim president, Katrina Armstrong, resigned and was replaced by Claire Shipman, a co-chair of the school’s board of trustees.

Some have welcomed the changes Columbia announced, which were already in progress before Mr. Trump’s demands as part of an effort to combat antisemitism. And Samantha Slater, a Columbia spokeswoman, defended the concessions to the White House.

“We will always uphold the university’s mission and values,” she said.

But the deal incited faculty protests and a lawsuit by faculty groups against the Trump administration saying that the planned cuts “represent an existential ‘gun to the head’ for a university,” according to the complaint.

Former Mayor Bill de Blasio, a Democrat, said institutions like Columbia and major law firms, which he called “pillars of America,” should be role models for resistance.

“When an institution fights back, it makes it easier for everyone else to fight back,” he said. “Giant law firms and a highly endowed Ivy League university — they’re going to be here long after Donald Trump. They have the resources to sustain a fight. If you give in on this one, there will be something else.”

A City’s Identity

New York has a long history of resisting presidents whose policies or actions were viewed as politically unfavorable or damaging to the city: Mr. Murrow called out Dwight D. Eisenhower’s tolerance of McCarthyism; Martin Luther King Jr. led huge protests against Lyndon B. Johnson’s support for the Vietnam War; and Gerald Ford’s refusal to bail out the city during a fiscal crisis in 1975 likely cost him re-election.

But today, some of the city’s strongest pillars are quivering.

“Now,” said Mark Levine, a Democratic candidate for city comptroller, “we’re the center of appeasement.”

The city has been a reliable Democratic stronghold for decades, so much so that some New Yorkers were shocked by Mr. Trump’s electoral gains in November’s presidential election compared with his performance in 2020.

But it’s also a city where adoration of capitalism gave rise to Wall Street billionaires and real estate scions like Mr. Trump himself. Now, some of the city’s leaders and thinkers are wondering whether the responses to Mr. Trump expose more of New York’s true identity.

“We are a city of rollovers, institutionalists who don’t want to rock the boat,” said Richard Flanagan, a political science professor at the College of Staten Island. “Deals before principles. A capitalist city before a progressive one.”

All the backing down has made the Rev. Al Sharpton question whether New York is as tough as he thought it was.

“You never know how strong you are until you’re tested,” he said, noting that civil rights protesters have learned that upholding values often comes at a steep cost. “If people really believed in what they stood for they wouldn’t capitulate. It makes me wonder if they ever believed in the first place.”

But while Mr. Trump’s detractors call him a bully, his supporters say his actions are nothing more than deal-making — that making demands and exerting leverage are the way things get done.

And Mr. Trump has gloated over his wins.

“You see what we’re doing with the colleges, and they’re all bending and saying: ‘Sir, thank you very much. We appreciate it,’” he said on Wednesday. “Nobody can believe it, including law firms that have been so horrible, law firms that, nobody would believe this, just saying: ‘Where do I sign? Where do I sign?’”

A President, a Mayor and a Dilemma

Perhaps no one has brought the ethical dilemmas engendered by Mr. Trump’s deals and demands into sharper relief than Mayor Eric Adams.

Facing corruption-related charges, Mr. Adams, a Democrat, sought to cozy up to Mr. Trump even before the election in what was widely criticized as an attempt to make his criminal case go away.

But when those efforts appeared to pay off, and a Trump appointee at the Justice Department sought to abandon the case against Mr. Adams, prosecutors and city officials found themselves confronted with a difficult decision.

Rather than cut bait on the case, the interim U.S. attorney, Danielle R. Sassoon, resigned, as did the case’s lead attorney, Hagan Scotten.

Mr. Scotten, who served three combat tours in Iraq as a U.S. Army Special Forces officer and earned two bronze stars, said in a resignation letter that only a fool or a coward would obey the order.

Ms. Sassoon, in her resignation letter, indicated that she believed Mr. Adams and the Trump administration were engaging in essentially a quid pro quo, with the mayor agreeing to help cooperate on the president’s immigration agenda in exchange for the dropped charges.

Concerns about the mayor’s indebtedness to the Trump administration led four deputy mayors to make their own difficult choice: Amid the controversy, concerned that Mr. Adams’s personal interests risked outweighing the interests of New Yorkers, they resigned.

The ramifications spread further. In Washington, five Justice Department prosecutors resigned rather than sign the motion to dismiss the case against Mr. Adams.

In the end, a veteran prosecutor, Ed Sullivan, agreed to file the request in order to save more of his colleagues from losing their jobs, according to three people briefed on the interaction. The judge overseeing the mayor’s case is still reviewing the request.

For some who have chosen to fight Mr. Trump’s demands, much hangs in the balance, and the outcome will not be clear anytime soon.

New York transit officials and Gov. Kathy Hochul have held firm during a standoff with federal officials over the fate of congestion pricing, which seeks to cut traffic and raise money for the Metropolitan Transportation Authority by charging drivers who enter Manhattan’s central business district.

As soon as Sean Duffy, the secretary of the U.S. Department of Transportation, sent a letter ordering the M.T.A. to shut down the program, the authority sued and has so far ignored the administration’s deadlines. And Ms. Hochul has invoked the action movie “Rambo” to suggest that Mr. Trump would pay for drawing “first blood.”

Donovan Richards, the borough president of Queens, where Mr. Trump was born, said officials couldn’t stop resisting a president who went against the values of many New Yorkers.

“We have to fight,” he said. “There is enough room for everybody to win here.”

Jonah E. Bromwich contributed reporting.