“This is what we told the voters we were going to do,” he said of the straightforward repeal effort.

Conservatives have become increasingly alarmed at discussion of what they deride as “Obamacare Lite” — efforts to keep some of the provisions in place and “repair” the health law rather than kill it outright. They complain that an approach backed by some House health policy writers would impose new taxes on employer-provided health insurance and interfere in a part of the marketplace that is working. And they don’t favor a tax credit plan that Mr. Trump endorsed in his speech. They back the more market-driven approach that Republicans approved in 2015.

But that legislation was crafted when President Obama was in office and was certain to veto any repeal — giving Republicans what amounted to a free shot at the law. Now they and their constituents would have to live with the replacement, and lawmakers fear a potential backlash if it goes awry. Many Republicans may have complained that the crowds at angry town hall meetings over the recent recess were organized by political opponents, but that doesn’t mean Republicans aren’t paying attention to them.

In the face of that nervousness, Mr. Paul is reminding Republicans that the main reason the party won election victories in 2010, 2014 and now 2016 was the clear promise to end the health care law.

“They didn’t tell us to repeal but to keep the Medicaid expansion,” Mr. Jordan said.

But just as conservatives are adamant that Republicans repeal the law before replacing it, other more centrist Republicans are threatening to withhold their votes if there is no suitable alternative in place. That division is creating a real headache for Republican leaders such as Speaker Paul D. Ryan of Wisconsin and Senator Mitch McConnell, the majority leader from Kentucky, who have to find something a majority will support.

They say they will eventually reach a solution, but they know they have serious problems at the moment. Mr. McConnell called a special Senate Republican meeting for Wednesday to hear from House committee chairmen on their plans and to try to hash out the sharp internal differences.

“The goal is for the administration, the House and the Senate to be in the same place,” Mr. McConnell said. “We’re not there yet. There’s a lot of discussion about how to craft that, what combination of legislation and regulation will get us to where we want to get.”

That is a far cry from confident pledges that the despised health insurance law would quickly be history once Republicans took power. Now conservatives, sensing backsliding among their colleagues, again want to use their numbers to dictate their desired result. Seems just like old times on Capitol Hill.