“If you’re going to fumble the ball,” he added, “better to do so in the first quarter of a football game.”
Devising health care legislation that could appeal to both wings of the House Republican Conference — the hard-line conservatives and more moderate members — would require a nearly superhuman feat, added Representative Billy Long, Republican of Missouri.
“Not unless Harry Houdini wins a special election to help us,” Mr. Long said about the prospects of cobbling together a coalition that could agree on how to repeal and replace the health care law.
But other longtime Republicans warned that if the party did not address what they have derided as Obamacare, an issue that has been central to their campaigns for the last seven years, they would incur a heavy political price in the midterm elections.
Midterm campaigns have increasingly become akin to parliamentary elections — referendums on the party in power rather than on individual candidates, where turnout by dependable partisan voters is the deciding factor.
“If they fall on their sword on this, they’re going to get slaughtered,” said former Representative Thomas M. Davis III, a Virginia Republican who himself was once at the helm of the House campaign committee.
“Where parties get hurt in midterms is when their base collapses,” Mr. Davis said. “Democrats are going to show up regardless of what you do. If our voters don’t see us fulfilling what we said we were going to do, they’ll get dispirited.”
What troubles many Republican strategists is the specter of the party’s most reliable voters being bombarded by reminders of their leaders’ failure to address the health law. They fear a recurring story line sure to pop up every time insurance premiums increase, providers leave local networks, or, most worrisome, Republicans fund President Barack Obama’s signature achievement.
Conservatives, many of whom opposed the House repeal bill, now warn that it is untenable to stand pat on the issue — and that lawmakers will face retribution if they do not return to the repeal-and-replace effort.
“If people are looking at a situation where there’s no action on this, there are going to be conversations about primaries,” warned Michael A. Needham, the chief executive of Heritage Action for America, the Heritage Foundation’s political arm, which worked to scuttle the Republican health bill last week.
That Republicans even find themselves in such a quandary just over two months after Mr. Trump was sworn in is at once extraordinary and not altogether surprising. Republicans who were then in office opposed the Affordable Care Act when it was enacted in 2010, yet they were paralyzed in efforts to undo it.
The paradox is predictable for a party that has been at war with itself since the final years of President George W. Bush’s administration. Mr. Trump transcended those divisions last year in his campaign, but congressional Republicans remain riven between their hard-liners and mainstream conservatives.
Perhaps it was inevitable that these factions would clash over an issue as sensitive as remaking the American health care system. The purists — often from politically safe districts — believe the government should play almost no role in providing health insurance to its citizens. Placating them without endangering more pragmatic lawmakers worried about depriving constituents of their health coverage may be an impossible task.
“I think we need to start negotiating with Democrats instead of the Freedom Caucus,” said a frustrated Mr. Stivers, referring to the most conservative bloc of House Republicans. “They don’t know how to get to yes.”
Democrats, though, have no appetite for conciliation: They see the Republican disarray over health care, and the broader tensions on display in the clash over the health care law, as a path back to the House majority.
Seizing on the Republicans’ American Health Care Act, which according to a Quinnipiac University survey last week was supported by only 17 percent of Americans, Democrats have started digital advertising against the 14 potentially vulnerable House Republicans who supported the legislation in committee votes.
Some of these lawmakers represent districts that Hillary Clinton carried last year. They are as concerned about the consequences of casting a vote for the bill as they are about inviting a backlash from their bases for not addressing the issue at all.
Indeed, though much of the frustration from mainline Republicans has been directed at the Freedom Caucus, Republican lawmakers from pro-Clinton districts played just as big a role in torpedoing the American Health Care Act.
“I don’t want to vote for a bill that has no chance of passing the Senate,” explained Representative Leonard Lance of New Jersey, one such lawmaker who invoked the haunting tradition of House members’ casting risky and, in some cases, career-ending votes, only to see their Senate colleagues sit on the proposals.
Mr. Lance, whose district Mrs. Clinton carried, and other Republicans insisted after the bill’s collapse last week that they still wanted to wrestle with the Affordable Care Act in this Congress.
But former Representative Earl Pomeroy of North Dakota, a Democrat who lost his seat in 2010 in part because of his vote for the Affordable Care Act, said he thought Republicans like Mr. Lance were actually “breathing a sigh of relief” for averting a floor vote.
“It’s a very, very tough vote for somebody in a competitive race,” Mr. Pomeroy said. “They may alienate their base by voting against it, but if they support a bill resulting in people losing their coverage, there will be electoral hell to pay.”