For Mr. Trump, the worry about approval ratings would be less about what it might mean for the next election, still years away, but about how such numbers are interpreted by members of Congress, who historically have been more deferential to popular presidents than unpopular ones.

“Every president starts off with a good-will account with Congress that eventually draws down,” said Phil Schiliro, who was Mr. Obama’s White House legislative director in his first term. “As approval ratings drop, the account sinks very quickly. And that makes it much harder to bring Congress along on the president’s priorities.”

Steve Israel, a Democrat who represented New York in the House, said the biggest challenge for Mr. Trump might be with nervous members of his own party. “Right now, Trump’s numbers are kryptonite for 21 House Republicans in districts that he lost,” he said. “So not only does he begin with low poll numbers, he begins with a significant potential bloc of resistance in his own caucus.”

But Mr. Trump has shown that he intends to lead more through force of personality than through the breadth of his coalition. Brash and uninhibited, he seeks out enemies and allows few slights to go unanswered. He has repaired bridges with some critics, like Mitt Romney, but has made only sporadic efforts to reach out to parts of the public that have not supported him.

His strongest supporters cheer his pugnacious style, and he argues that it has gotten results, like when House Republicans backed off plans to undercut the authority of the Office of Congressional Ethics, or major employers reversed plans to move jobs overseas after he wrote on Twitter about his disapproval.

“With all of the jobs I am bringing back into the U.S. (even before taking office), with all of the new auto plants coming back into our country and with the massive cost reductions I have negotiated on military purchases and more, I believe the people are seeing ‘big stuff,’ ” Mr. Trump wrote on Twitter on Tuesday.

For many years, presidents and their advisers quaked at polls that showed a drop in their ratings, fearful that it would hurt their ability to command the stage and to enact their agendas. The last two presidents governed for long stretches with less than majority support, which clearly limited their capacity to advance major legislation. But they both also demonstrated that they could still make at least some progress.