WASHINGTON — Two more Senate Republicans declared their opposition on Monday night to the latest effort to overhaul the nation’s health care system, leaving the measure without sufficient support to pass and potentially ending a months-long effort to make good on a longstanding GOP campaign promise.

Republican Senators Mike Leeof Utah and Jerry Moran of Kansas issued statements declaring that they would not vote for the revamped measure. They joined Republican Senators Rand Paul of Kentucky and Susan Collins of Maine in opposition. With just 52 seats, Republicans can afford to lose only two votes to pass their proposed rewrite of the Affordable Care Act. All 48 Democrats are expected to vote against it.

‘‘In addition to not repealing all of the Obama-care taxes, it doesn’t go far enough in lowering premiums for middle class families; nor does it create enough free space from the most costly Obamacare regulations,’’ Lee said in a statement.

Moran said the bill ‘‘fails to repeal the Affordable Care Act or address health care’s rising costs.’’

By jumping together, Moran and Lee ensured that no one would be the definitive “no’’ vote.

With four solid votes against the bill, Republican leaders were faced with two options: go back and try to rewrite the bill in a way that could secure 50 Republican votes, a seeming impossibility at this point, or do as Senator Mitch McConnell, the Republican leader, had promised and team with Democrats to draft a narrower, bipartisan measure to fix the flaws in the Affordable Care Act that both parties acknowledge.

The Senate Democratic leader, Chuck Schumer of New York, responded to the announcement by urging his Republican colleagues to begin anew and, this time, undertake a bipartisan effort.

“This second failure of Trumpcare is proof positive that the core of this bill is unworkable,’’ Schumer said, according to The New York Times. “Rather than repeating the same failed, partisan process yet again, Republicans should start from scratch and work with Democrats on a bill that lowers premiums, provides long-term stability to the markets, and improves our health care system.’’

Senate Republican leaders returned to the Capitol on Monday still pledging to press ahead with plans to pass a sweeping overhaul of the nation’s health-care system, but the news of Lee and Moran digging in against the bill created the deepest doubts yet as to whether it could pass.

The day had already begun with uncertainty as the health of Senator John McCain thrust the future of the flagging effort deeper into doubt.

In a speech on the Senate floor, McConnell said that he spoke with McCain on Monday morning and that ‘‘he’ll be back with us soon.’’ The Arizonan is recovering from surgery to remove a blood clot above his left eye that involved opening his skull.

McConnell has delayed action on health care until McCain’s return. While McConnell has no way to pass the legislation without his vote, McCain’s presence in the Capitol is far from a guarantee that it will succeed.

McCain had voiced worries about the measure and has not committed to voting for it.

In his speech, McConnell said Republicans intend to put in ‘‘continued hard work’’ to pass their proposed rewrite of much of the Affordable Care Act.

But the likely timetable remained unclear. McCain, 80, is awaiting results of tissue pathology reports ‘‘pending within the next several days,’’ the hospital treating him said in a statement over the weekend.

He will be away from the Senate for at least the rest of the week. A McCain spokeswoman had no further update on his condition Monday.

Republican Senator Lindsey Grahamof South Carolina, perhaps McCain’s closest friend in the Senate, spoke to him by phone as he was walking to the Senate chamber for a vote Monday evening. The two had an animated conversation, and Graham said McCain was eager to get back.

‘‘They were doing a routine checkup and they found the spot and it looks like everything is going to be A-OK,’’ Graham said.

He said McCain’s doctors ‘‘don’t want him to fly for a week,’’ adding, ‘‘I think he would walk back if they would let him.’’

The cause of McCain’s blood clot remained unclear on Monday.

Senate Republicans are under self-imposed pressure to complete their work on health care soon. As they have struggled to show progress, McConnell has already said he will keep the chamber in session through the first two weeks of August, postponing the start of the summer recess period to leave time to work on other matters.

Key Republican senators - and the GOP governors they turn to for guidance - have raised concerns about how the bill would affect the most vulnerable people in their states. Private lobbying by the White House and Senate GOP leaders has not mollified them.

President Trump planned to huddle with seven Republican senators at the White House Monday evening to talk about health care, including top McConnell allies such as Senators John Cornyn of Texas, John Thune of South Dakota, Roy Blunt of Missouri, and Lamar Alexander of Tennessee.

Material from The New York Times was used in this report.