“Part of Trump’s ability to dodge bullets in the past has rested on his ability to change the subject,” Geoff Garin, a Democratic strategist and pollster. “And this time he’s changing his story instead of changing the subject. And we’re now several days into a very negative narrative on Trump’s conduct in his dealings with Putin.”

If aware of the risks he was taking, Mr. Trump, an obsessive over ratings and approval numbers, seemed unconcerned. Though a majority of Americans disapprove of how he handled himself in Helsinki, 68 percent of Republicans are sticking by him, according to a CBS poll released on Thursday. And a poll conducted by the news site Axios and SurveyMonkey showed that 79 percent of Republicans approved of the meeting.

Mr. Trump has generally met criticism over his behavior with the pugilistic response he has sharpened over his 72 years, first as the child of a wealthy real estate developer, a tabloid fixture, a reality TV star and now from his seat in the Oval Office. It has never stopped him — not for long, anyway.

“I think his willingness to double down in the wake of these events that everyone else sees as catastrophic is because he authentically doesn’t care,” Timothy O’Brien, the author of the 2005 book “TrumpNation: The Art of Being the Donald,” said in an interview. “He’s been insulated his whole life from the impact of his own mistakes.”

But Whit Ayres, a Republican pollster, noted that Mr. Trump’s base of support had endured through Charlottesville and the border separation crisis. “Politics has become so polarized that there is a powerful tendency to rally around our guy,” Mr. Ayres said, “and to defend our guy in the face of criticism from people we don’t like.”

But Mr. Garin, the Democratic strategist, said that by continuing to show a conciliatory side to Mr. Putin, the president was “making it harder and harder for Republicans to defend him with any real conviction.

“And that may signal to voters that there’s something different about this one,” he added.

With his invitation to Mr. Putin, the president again appeared in tune with the Russian president, who, in a foreign policy speech to Russian ambassadors, appeared to be channeling the views of his American counterpart.