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.”