But there was no hint of an olive branch from the Senate majority leader, Mitch McConnell, who this summer suggested that a failure to repeal the Affordable Care Act would force him to work with Mr. Schumer.

“Bailing out insurance companies with no thought of any kind of reform is not something I want to be part of,” Mr. McConnell said in the early hours of Friday. He suggested that many Democrats secretly wanted a single-payer health care system, with a much larger role for the government.

President Trump reiterated his threat to force the health law to collapse. “3 Republicans and 48 Democrats let the American people down. As I said from the beginning, let ObamaCare implode, then deal. Watch!” he wrote on Twitter.

And some Republicans did not sound ready to close the door on repeal, despite the exceedingly slim hopes of reviving, yet again, an effort that on Friday morning seemed doomed.

“I am disappointed and frustrated, but we should not give up,” said the House speaker, Paul D. Ryan of Wisconsin. “I encourage the Senate to continue working toward a real solution that keeps our promise.”

If a bipartisan coalition can coalesce around changes to the Affordable Care Act, lawmakers see several vehicles to force such proposals to the floors of the House and Senate. Spending bills for the fiscal year that starts Oct. 1 will have to be signed, and the popular Children’s Health Insurance Program will need additional funds.