At the lunch, Mr. Trump mixed threats of political retaliation against Republicans who crossed him with pleas to move ahead with a long-promised repeal-and-replace legislation, urging senators to remain through their August recess if necessary. It was a stark change from his earlier promise to let the health care law collapse and let its beneficiaries face the consequences.

“My message today is really simple,” Mr. Trump told them. “We have to stay here; we shouldn’t leave town, and we should hammer this out and get it done. And not just a repeal,” he said, conceding he had backed that idea before. “I think the people of this country need more than a repeal. They need a repeal and a replace.”

That was good news to Senator Shelley Moore Capito of West Virginia, who had been one of the first Republican senators to balk at moving ahead on an outright repeal plan, along with Senators Susan Collins of Maine and Lisa Murkowski of Alaska.

“I’m glad @POTUS agrees that we cannot move to repeal Obamacare without a replacement plan that addresses the needs of West Virginians,” Ms. Capito said on Twitter.

It is difficult to say how much she and other Republicans — whom Mr. McConnell described as having “some difficulty in getting to yes” — were persuaded by the president’s appeal. But with several days remaining before a vote, Republicans were finding it hard to resist the call to at least make the effort to find some resolution, though many were very skeptical of the chances for success.

The window remaining before the vote also allows both opponents and proponents of the Republican health proposals to step up their pressure on key lawmakers, and they will face an assault.

A coalition of conservative advocacy groups took a harsh line against Republicans who were threatening to derail the health care effort, promising to initiate primary campaigns against them. They noted that all Republican senators who were then in office, except for Ms. Collins, had voted for a vetoed 2015 repeal plan that would be on the floor next week and that the party had campaigned endlessly on its promises to kill the Obama health care law.