There is one thing a president can do when Congress is an ungovernable mess, polling numbers are blinking red and crises abroad show no signs of resolving themselves. And that thing is: get out of town.

President Biden traveled to New York on Wednesday to headline three fund-raisers, where he presented himself as the last line of defense against the re-election of Donald Trump and as a dedicated — if imperfect — leader who had been around long enough to recognize the existential threat Mr. Trump poses to democratic institutions, including the presidency.

“It is dangerous for us to be engaged in this kind of politics, because it ends up dragging us all to the bottom,” Mr. Biden said during his third reception, where his voice had lowered to a whisper after a day of shaking hands, taking selfies and delivering speeches.

“It’s not that I’m so good, but you have to have someone who can beat somebody.”

Mr. Biden also pre-empted criticism of his age by joking that he was not 81, but “40 times two.” But in the drawing rooms and ballrooms of New York City, any enthusiasm for a second Biden term seemed to be mingled with fear about the thought of a second one from Mr. Trump.

“We’re here for him, and for the next four years,” said Maureen White, a Democratic donor and the host of Mr. Biden’s third reception of the day, as she stood next to the president. “But we’re also here because the consequences of not electing Joe Biden are terrifying.”

Hoping to hit all of the targets, from policy-focused activists to community health care workers who had shouldered the brunt of the coronavirus pandemic, the Biden campaign organized three distinct events on Wednesday. The first was a small, climate-focused panel on the Upper West Side. The second, a large reception with Latino supporters at the Mandarin Oriental.

The third was held in an opulent residence across the street from the Metropolitan Museum of Art. Manhattanites, including the actor Robert DeNiro, attended, with risotto, chicken satay and coconut shrimp on the menu. A small Israeli flag stood among the artwork.

At each event, Mr. Biden retooled his message for the crowd, but largely focused on Mr. Trump. Several times, Mr. Biden diverged from his original point in a story about his upbringing or decades in Congress. By the end of the day, he was recounting a request to deliver Senator Strom Thurmond’s eulogy while talking about the Republican Party.

”They didn’t change their views, but there was a sense, as strange as it sounds, of civility,” Mr. Biden said, recounting his work with Mr. Thurmond and other segregationists. “The point is, we’ve changed drastically.”

At all three events, Mr. Biden largely stayed away from the war in Gaza, and though protests were barely visible from the presidential motorcade, people angry over his support for Israel’s campaign against Hamas had gathered to demonstrate at different points throughout the city.

No president enjoys protesters, and Mr. Biden was kept away from the people who came waving Palestinian flags — people who are also part of the base he needs to keep intact during an election year. Both the president and administration officials have responded to them carefully.

Karine Jean-Pierre, the White House press secretary, told reporters aboard Air Force One en route to New York that protesters had the right to “make sure their voices are heard in a peaceful way. We support that. The president supports that. You hear the president when — when situations do occur.”

At one point, when Mr. Biden arrived at the Mandarin Oriental to speak to a large group of Democrats, many of them affiliated with SOMOS, a Latino-led community health group, protesters had gathered 35 floors below.

A crowd that one police officer estimated at about 100 people assembled at Columbus Circle to protest the Biden administration’s support for Israel during the country’s war with Hamas. Several voters who consider themselves Democrats or left-leaning and had voted for Mr. Biden in 2020 said they felt unhappy with him and were reconsidering voting at all.

Sam Skinner, a 24-year-old who lives in Queens, said that he voted for Mr. Biden in 2020 but that the president’s handling of the war had made him rethink whether he’d vote for him again.

“I do think he is genuinely a dangerous person to have as president,” Mr. Skinner said of Mr. Trump, “but right now Biden seems like the danger, actively endangering peoples’ lives.

“I feel like the Biden strategy seems to be right now waiting for Trump to say something super insane and come across as chaotic,” Mr. Skinner added.

Republican-wrought chaos was indeed Mr. Biden’s main focus. According to Democratic donors, the strategy is a moneymaker: Mr. Biden’s campaign reported having about $46 million in cash on hand at the end of December, compared with $33 million for Mr. Trump’s campaign, according to filings on Wednesday to the Federal Election Commission.

At multiple points during his visit to New York, the president excoriated Mr. Trump for pressuring Republicans to abandon a deal on the border. He chastised Republicans for turning away from supporting Ukraine in its efforts to beat back a Russian invasion: “What are we doing? Stepping back?”

He turned to an often-repeated story on his decision to enter the 2020 presidential race, which came after Mr. Trump refused to condemn a group of white supremacists who held a rally that turned deadly in Charlottesville, Va. And he twice criticized Mr. Trump’s remarks after a school shooting in Iowa in January in which the former president told a crowd that it should “get over” the shooting.

“Just get over it?” Mr. Biden said, raising his voice to a yell. “What the hell is he doing?”

Earlier in the day, protests over Gaza were not detectable from the wood-paneled drawing room of Larry Linden, a philanthropist and climate activist who was the managing director of Goldman Sachs. Standing next to the president, Mr. Linden told a crowd of supporters gathered at his home on the Upper West Side that Mr. Biden “seems to excel at practically everything,” including pulling the United States out of the coronavirus pandemic, all “while maintaining your integrity, decency, faith and likability.”

(A smiling Mr. Biden gamely shook his head at the “excels at everything” part.)

In a later email, Mr. Linden praised the president for his efforts to help the environment, and said that it risked unraveling should he lose in November.

“He has done more to tackle the climate challenge than any other president, ever,” Mr. Linden wrote. “And his likely opponent has made a loud, public commitment to undermine all of those gains, placing the nation and the planet in great peril.”

Liset Cruz and Julian Roberts-Grmela contributed reporting.