Indeed, Mr. Trump’s Twitter posts have become the communications equivalent of a mother who threatens to cancel the family vacation if her children do not unload the dishwasher — a noteworthy threat, but most likely empty. “Oddly enough, I think it’s fairly banal,” said Representative David Schweikert, Republican of Arizona and a member of the Freedom Caucus. “We are used to it. It goes with the job. He is not the first president who has attacked us, just the first from our own party.” Asked if he expected the White House to work closely with the group on further legislation he said, “The answer is yes.”

Mr. Trump’s Twitter account has long been seen as fear-inducing political weapon. And his message Thursday was the sort of warning shot many Republicans thought could be fired to enforce party discipline. But it seemed to have the opposite effect.

The reasons Mr. Trump’s threats may well have about as much bite as a catfish — scary appearance, weak teeth — are many.

The health care bill that the many House members rejected was extremely unpopular. Only 17 percent of Americans supported the proposal, according to a Quinnipiac poll released last week. Even among Republicans, the repeal-and-replace measure was barely tolerable: Just 41 percent of Republicans in the same survey said they approved of the bill. Many voters in states that Mr. Trump won benefit from the Affordable Care Act, derided as Obamacare, particularly in states that have expanded the Medicaid program.

In the most conservative districts where Mr. Trump may target lawmakers, such as that of Mr. Sanford, voters are likely more in sync with their representatives, who felt the rollback of the law did not go far enough, than their president, who simply wanted a win.

“These are not people subscribed to the Heritage Foundation,” Mr. Sanford said, referring to the conservative research group that opposed the Republicans’ doomed effort to repeal and replace the Affordable Care Act. “They’re not part of the intelligentsia of what happens in Washington. They’re just conservative folks.”