The president insisted that he maintained “tremendous” Republican support, even as nearly a half-dozen Republican senators have said directly or strongly suggested that they wanted to reopen the government, then have the debate about the wall.

“I think we have tremendous Republican support,” Mr. Trump said. “The Senate has been incredible. Mitch McConnell has been incredible,” he said, referring to the Senate majority leader.

The president, who has refused to sign any bill to fund the government that does not include $5.7 billion for the wall, also said some Democrats were moving to his point of view, although he did not offer any names.

“The fact is that there is tremendous support,” he said.

“If I did something that was foolish, like gave up on border security, the first ones that would hit me would be my senators — they’d be angry at me,” he said. “The second ones would be the House. And the third ones would be frankly my base and a lot of Republicans out there and a lot of Democrats that want to see border security.”