Now, Mr. Trump and his Republican allies on Capitol Hill have recast their ambitions for a rapid-fire repeal, talking privately and publicly about a more deliberative process that could be phased in over weeks or months.

“The political uncertainty surrounding repeal is growing,” said Dan Holler, a spokesman for Heritage Action for America, the advocacy arm of the conservative Heritage Foundation. “If the House has not passed a repeal bill and sent it to the Senate by mid-March,” Mr. Holler added, “that would be serious cause for concern.”

The uncertainty is already reflected in the way Republicans talk about the health care law. Some now talk about “repairing” the law, rather than repealing it entirely. And in a twist of fate, many are facing tough, angry questions at town hall meetings — the mirror image of 2009, when Tea Party activists assailed Democrats who supported the law.

A crowd of protesters gathered outside a town meeting in California held over the weekend by Representative Tom McClintock, who was escorted by police officers as he left the event, according to news reports. Representative Gus Bilirakis of Florida faced 200 angry supporters of the health care law at a meeting on Saturday.