Ambling onto the Art Deco set of “The Tonight Show” for his monologue rehearsal one Monday afternoon, Jimmy Fallon gave the crowd here at Studio 6B a warm, practiced welcome before trying out a new batch of jokes about the French election, the pop star Harry Styles and President Trump’s definitions of medical terms. “He thinks a cardiologist is someone who works at Hallmark,” he quipped.

Wearing casual clothes and a boyish smirk, Mr. Fallon made a pitch for his program’s vision. “Anything I can make fun of, I will make fun of,” he told his audience. The late-night entertainment being fine-tuned in front of them, he added, had been devised so that “you go to bed with a smile on your face and you have sweet dreams.”

Then he stepped to the spot where he delivers his monologue each evening and noted that the stage mark was in the shape of a four-leaf clover. “I’m Irish,” he explained, “and I need all the luck I can get.”

It was a throwaway, self-deprecating line, but also an accurate self-assessment from Mr. Fallon, 42, who is in his fourth year of hosting “The Tonight Show,” NBC’s flagship late-night program.

He is weathering the most tumultuous period in his tenure there — a predicament for which he has himself to thank, and one that raises the question of whether the multitalented but apolitical Mr. Fallon can ride out the current era of politicized, choose-your-side entertainment, when he just wants to have a good time.

Once the undisputed juggernaut of the late-night category, Mr. Fallon’s “Tonight Show,” a celebrity-friendly cavalcade of games and gags, has seen its ratings decline in recent months. Meanwhile, his politically pointed competitor Stephen Colbert, who hosts CBS’s “The Late Show,” has closed what was once a formidable gap of nearly one million viewers.

The resurgent interest in left-leaning programming  hasn’t helped Mr. Fallon, a former star of “Saturday Night Live” who has built his brand on his all-around entertainer’s skills and down-the-middle tastes. And as Mr. Fallon is well aware, viewers haven’t seen him in quite the same light since  an interview he conducted with Mr. Trump in September , which was widely criticized for its fawning, forgiving tone. In a gesture that has come to haunt the host, he concluded the segment by  playfully running his fingers through Mr. Trump’s hair.

Mr. Fallon acknowledges now that the Trump interview was a setback, if not quite a mistake, and he has absorbed at least a portion of the anger that was directed at him by critics and online detractors.

“They have a right to be mad,” a chastened Mr. Fallon said in an interview this month. “If I let anyone down, it hurt my feelings that they didn’t like it. I got it.”

But if these events prompted Mr. Fallon to search his own soul, he said they did not compel him to make widespread changes at “The Tonight Show.”

The program is still profitable and strongly supported by advertisers, so if Mr. Fallon faces any crisis, it’s an existential one: What if the broader shift to a more partisan, more openly anti-Trump late-night isn’t temporary? If it has a longer life and a bigger impact than anyone foresees, what does he want his show to be?

As strongly as ever, Mr. Fallon believes it should be a place for a wide swath of viewers to get their entertainment and laughs, and that this philosophy will steer it through a period of intense polarization.

“I don’t want to be bullied into not being me, and not doing what I think is funny,” he said more defiantly. “Just because some people bash me on Twitter, it’s not going to change my humor or my show.”

He added: “It’s not ‘The Jimmy Fallon Show.’ It’s ‘The Tonight Show.’”

Late one evening, Mr. Fallon was in his sixth-floor corner office at NBC’s Rockefeller Center headquarters. The room was lit by the neon of the Radio City Music Hall sign while he played a party game on his PlayStation 4 with several of his writers.

In an editing suite, finishing touches were being made to a segment in which Mr. Fallon, Kevin Bacon and the country singer Chris Stapleton  impersonated the Texas rock band ZZ Top . Before the taping, a guitar that was supposed to spin around Mr. Stapleton’s waist had broken, and Mr. Fallon was hoping there was footage from their dress rehearsal to cover this up.

This is the kind of crisis that Mr. Fallon likes to deal with. He gets a similar thrill from the daily creative meetings in his office, where writers share their progress on projects like a video in which the Smash Mouth song “All Star” is  recreated with dialogue from “Star Wars” movies .

The segments he loves best, Mr. Fallon said, are dispensable morsels of “brain candy — when people go, ‘That’s cool that they put this much thought into such a dumb, silly bit.’”

There was a time when Mr. Fallon’s  lip-sync battles  and  facetious thank-you notes  gave “The Tonight Show” dominance. At the end of 2016, it was handily winning its 11:35 p.m. time slot with around 3.5 million viewers a night.

Not five months later, Mr. Colbert usually surpasses Mr. Fallon in overall nightly audience; in a recent week, Mr. Colbert drew more than three million viewers, while Mr. Fallon had just under 2.7 million. “The Tonight Show” has continued to win the coveted 18-to-49 demographic that is specially valued by advertisers.

Mr. Fallon claims he pays no attention to these metrics. “We’re winning in something,” he said. “People in the height requirement between 5-7 and 5-11, we’re No. 1, from 11:50 to 11:55.” More emphatically, he added: “I never, ever care. I’ll know when someone fires me.”

Even so, in recent weeks, as Mr. Colbert has drawn headlines for  a lewd joke  about Mr. Trump and the Russian president, Vladimir V. Putin; and Jimmy Kimmel, the host of ABC’s “Jimmy Kimmel Live!,” has touched off a political debate by  sharing the story  of his newborn son’s heart surgery, there is a sense that Mr. Fallon cannot command the zeitgeist as easily as he used to.

During long taping breaks at “The Tonight Show,” Mr. Fallon likes to regale his studio audience with tales of his childhood: growing up in Saugerties, N.Y., where his dad used a key to scratch out the swear words on his Rodney Dangerfield albums, and the impression competition he won as a teenager at a club in Poughkeepsie, N.Y.

Off camera, he has a more cutting, fatalistic sense of humor than he displays on TV. When I asked him about the recent maelstrom of criticism that Mr. Colbert faced, Mr. Fallon quipped: “I shouldn’t have started  the hashtag #FireColbert . Looking back on it, I went too far.”

But as much as any other virtue or quality he possesses, what has lately come to define Mr. Fallon is his interview with Mr. Trump from Sept. 15.

That day had been a particularly contentious one for Mr. Trump, then the Republican presidential nominee:  In a Washington Post interview , he refused to say that President Obama was born in the United States, and his son Donald Jr. was being criticized  for saying  “they’d be warming up the gas chamber” if Republicans behaved as Democrats did.

Mr. Fallon’s questions, however, were mostly innocuous; he asked Mr. Trump why children should want to grow up to be president and if his business background had helped him in the campaign. Their conversation concluded with Mr. Fallon fulfilling his longstanding wish of ruffling Mr. Trump’s hair.

“I didn’t do it to humanize him,” Mr. Fallon said, explaining this moment to me. “I almost did it to minimize him. I didn’t think that would be a compliment: ‘He did the thing that we all wanted to do.’”

Once the interview was broadcast, Mr. Fallon said, “It all started going crazy.” A barrage of negative social media posts gave way to damning appraisals  in publications like Variety , where the critic Sonia Saraiya asked: “Who wouldn’t Fallon interview with such fawning, giggly acceptance? Where would he draw the line?”

She added, “How long will it take before American audiences lose all their faith in him, as an honest person they can watch every night?”

Lorne Michaels, the creator of “Saturday Night Live” and executive producer of “The Tonight Show,” said that at the time of Mr. Trump’s “Tonight Show” visit, he was regarded incorrectly as a presidential also-ran.

“I don’t think anybody was focused on him winning, or that possibility,” Mr. Michaels said. “It had been absolute, bedrock certainty that Hillary Clinton was winning that election. There was no doubt, certainly in the news department in our building.”

Accusations that Mr. Fallon was helping to normalize an extremist candidate spread rapidly, just as they had when Mr. Michaels invited Mr. Trump  to host “Saturday Night Live” in 2015 .