WASHINGTON — The House is expected to give final approval Friday to a measure that would allow Republicans to speedily gut the Affordable Care Act with no threat of a Senate filibuster, a move that would thrust the question of what health law would come next front and center even before President-elect Donald Trump takes office.

House approval would come after the Senate narrowly approved the same measure, a budget blueprint, in the pre-dawn hours Thursday. Americans woke up Thursday to the realization that a Republican Congress was deadly serious about eviscerating President Obama’s signature domestic achievement — a move that could leave 20 million Americans unsure of their health coverage and millions more wondering if protections offered by the Affordable Care Act could soon be taken away.

“This is a critical step forward, the first step toward bringing relief from this failed law,’’ Senator Mitch McConnell of Kentucky, the majority leader, said.

Democrats said the headlong rush to repeal was the height of legislative irresponsibility and would endanger the health of millions.

“For the life of me, I can’t understand the need to take health care away from people, and why in the world anybody would even contemplate doing that without something to replace it,’’ said Representative Louise M. Slaughter of New York. “Just snatching it out from under them and it’s gone. I think that there’s going to be a mighty rumble in this country, an outburst of anger and fear.’’

What comes next may be the most pressing problem facing Republicans, who may find that dismantling the law is far easier than replacing it with one that can unite their fractious members — and win over some Democrats.

After a marathon voting session, the Senate voted 51 to 48 to approve a budget blueprint that would clear the way for the health care law to be repealed with a simple Senate majority. As the House approached its vote, some Republicans remained reluctant to approve the budget measure without a clear strategy to replace the health law.

“We’d like to see a little more flesh on the bone before we sign on the dotted line,’’ said Representative Andy Harris of Maryland, an anesthesiologist and a member of the conservative House Freedom Caucus.

Republicans skeptical of moving forward risked looking hostile to the repeal effort. And there was a prevailing sense of the importance of following through on a campaign promise upon which so many House Republicans had staked their political reputations.

Republican leaders sought to reassure members that the House budget vote — procedurally important as it is — is only the first step in an exhaustive process to repeal and replace the Affordable Care Act. Four committees in the House and Senate would then be tasked with drafting the legislation that would gut the existing health law.

But Republicans face a significant challenge in passing the necessary legislation to replace the health care law. They can repeal major parts of the existing law without facing a filibuster, but they would not be able put in place a full replacement in the same measure, because arcane budget rules limit what can be included in such a filibuster-proof bill.

Instead, they would almost certainly need to pass another bill or several bills with 60 Senate votes, and that would require at least some Democratic cooperation.

Republicans in Congress have offered many replacement ideas, but it is not clear whether their most conservative members will ever be able to agree on legislation acceptable to the party’s moderates.

A manifesto issued by House Republicans in June outlined a consensus proposal, produced by the chairmen of four House committees, including Representative Tom Price of Georgia, chosen by Trump to be secretary of health and human services.

Trump and congressional leaders said they were counting on Price to help them write a replacement for the Affordable Care Act, most likely drawing from a bill he introduced in July 2009 and has reintroduced several times since.

Senate Republicans do not have a detailed plan. But Senator Lamar Alexander of Tennessee, chairman of the health committee, laid out a road map on the Senate floor this week that pointed to a measure potentially more expansive than House plans.

The major Republican proposals have not been analyzed by the Congressional Budget Office, so no independent or authoritative estimates exist of their costs or the number of people who might gain or lose coverage.