Mr. McConnell has expressed mounting frustration at the inability of the unified Republican government to make progress on health care and other issues.

“The American people said, ‘We elected a Republican president, a Republican House and a Republican Senate and we want to see some results,’” he told an audience in Kentucky over the recess. “And I can’t say anything other than I agree with you. But it is not easy, and we are going to continue to wrestle with this and try to get it done.”

“No action is not an option,” he emphasized. That remark seemed aimed at quelling calls to simply repeal the law, an alternative that faces steep procedural obstacles because it would require Democratic votes and Democrats will not provide them.

On Thursday, Mr. McConnell again suggested that Republicans might find themselves in negotiations with Democrats on a modest plan to shore up the existing health insurance exchanges if they cannot advance their own legislation. His comment both laid the groundwork for a defeat while trying to provide an incentive for Republicans to get behind the leadership plan.

The health care fight does not play to Mr. McConnell’s typical strengths. It is an extremely complex policy matter, and Mr. McConnell has often reveled more in tactics and procedure than the arcana of community rating and adverse selection.

Even some fellow Republicans acknowledge that Mr. McConnell’s refusal to allow hearings on the health care proposal has backfired, denying Republican lawmakers the opportunity to hear from experts, gauge the strengths and weaknesses of the legislation, and discern potential lines of attack as well as the support for any changes.

Republicans are finding how constituents respond when Congress tries to take a benefit away. The closest comparison might be the decision in 1989 to repeal a new Medicare catastrophic coverage law.