The Senate rejected a proposal Wednesday that would have repealed major parts of the Affordable Care Act and provided a two-year delay for lawmakers to develop a substitute, indicating that in the immediate future Republicans can only muster a majority for modest changes to the current law.

In two separate votes over the course of less than 24 hours, lawmakers have rejected different approaches to rewriting the landmark 2010 law known as Obamacare. But many Republicans have expressed an openness to passing a minimalist measure that abolishes two of the ACA’s insurance mandates and a single tax on medical devices, which is being dubbed “skinny repeal.”

GOP leaders have emphasized it is a way for the Senate to start negotiations with the House, and perhaps the one way they can sustain their seven-year drive to dismantle the health care law.

Several lawmakers acknowledged Wednesday that they did not embrace the content of the proposal, but suggested they could possibly back it anyway.

“It’s a vehicle to get us into conference,” said Sen. Lindsey Graham, R-S.C. “That is not a solution to the problem.”

But there did not appear to be an alternative solution for Republicans, who remain deeply divided over how to revamp the nation’s health care system. The GOP has little margin for error since just three defections within their ranks will deprive them of the 50 votes they need to pass legislation with the assistance of Vice President Pence, who can cast a tiebreaking vote.

On Tuesday night, just hours after opening debate, Senate Republican leaders were unable to pass a bill that they had spent weeks crafting but that never gained sufficient traction with the rank and file.

The fact that some Republicans have joined with Democrats on each of the votes so far underscored the challenge Senate leaders face in building consensus in coming days.

Fifty-seven senators – including nine Republicans – opposed the updated version of the measure known as the Better Care Reconciliation Act (BCRA), while 43 supported it. The nine dissenters included hard-line conservatives such as Sens. Mike Lee, R-Utah, and Rand Paul, R-Ky., as well as centrists like Sens. Dean Heller, R-Nev., and Susan Collins, R-Maine.

A subsequent move to abolish much of the ACA outright appealed to conservatives, but lost the backing of several moderates and also more establishment figures, such as GOP Sens. John McCain, Ariz., and Lamar Alexander, Tenn., who chairs one of the key committees that would normally craft a health-care bill. Overall, seven Republicans voted against that proposal.

Given all the disagreement, Republicans are focused on passing narrower changes to current law by the end of the week, known as “skinny repeal,” in hopes of keeping the debate alive in a House-Senate conference.

Opening the Senate on Wednesday morning, McConnell praised lawmakers for taking a “critical step” in opening the debate on health care. He signaled a difficult road ahead in the coming days.

“This certainly won’t be easy. Hardly anything in this process has been,” McConnell said.

Asked by reporters Wednesday whether enough Republicans could support a scaled-back bill at the end of this extended voting process, Senate Majority Whip John Cornyn, R-Texas, replied, We’ll find out.”

“This is a high-wire act – the whole thing,” Cornyn said.

There is some hope that the debate can begin anew, and perhaps include consideration of measures rejected on the Senate floor this week.

“When you get all done with it in a conference committee, you can come back in and take the most popular items that are out there and put them back in to the bill if they gain you votes or if they really improve the bill,”‘ said Sen. Mike Rounds, R-S.D., after Tuesday’s vote.

Several senators emphasized they feel a strong imperative to deliver some sort of health-care accomplishment, after vowing for seven years to unwind the health-care overhaul that president Barack Obama ushered into law with only Democratic support.

Sen. Bill Cassidy, R-La., who had raised objections earlier this month about Senate leaders’ proposal to make deep cuts in Medicaid, said he could back a more modest measure as long as he thought it represented some sort of improvement over the current law.

The “skinny repeal” option would repeal the ACA’s mandates that individuals buy plans and that employers with 50 or more employees provide coverage, said lobbyists and Senate aides, as well as eliminate the law’s tax on medical device manufacturers.

“My endgame is to have something that is fair to patients across the country,” Cassidy told reporters Tuesday night. “Now, I’m not quite sure how we get there, but I am all for anything that gets us one step closer to that end game.”

Still, both supporters and critics of GOP leaders’ strategy said there was no way to predict what sort of legislation they could produce, and the mood among Republicans was far from the buoyant excitement that some expected to accompany the first votes to fulfill their long-standing promise to repeal the ACA. Instead, GOP senators described feeling frustrated and unhappy with the legislative options at hand.

“The mood is nothing,” Sen. Bob Corker, R-Tenn., told reporters following Tuesday’s failed vote on the Senate GOP health-care bill. “It’s perfunctory.”

Or as Sen. James Lankford, R-Okla., put it in an interview: “There’s not a good option that’s sitting in front of us. There’s a process to get to a good option.”

And the Republican infighting that has dominated the health-care debate showed no signs of abating. Sen. Lisa Murkowski, Alaska, one of just two Republicans to vote against the motion to proceed, said late Tuesday that “there’s been a lot of discussion about” a scaled-back bill, but no definitive proposal.

“We’ll try to get down to where we can find that agreement, but I don’t know if any of us have identified what that may be,” she said.

President Donald Trump, for his part, took to Twitter on Wednesday morning to criticize Murkowski for not voting to start debate. “Senator @lisamurkowski of the Great State of Alaska really let the Republicans, and our country, down yesterday. Too bad!” he tweeted.

On Wednesday, the Senate was scheduled to vote on at least one repeal proposal, by Sen. Rand Paul, R-Ky., that would eliminate large parts of the ACA and impose restrictions on federal funding for abortion services. It is also expected to consider an amendment by Sen. Joe Donnelly, D-Ind., that would send health-care legislation back to committee for further consideration.

Democrats hope the vote on their amendment will give particular discomfort to Republicans like Sen. John McCain, Ariz., who complained that the GOP bill was written in secret by a small number of senators.

Republicans warned that the voting schedule could change at any time, however.

Democrats signaled that they won’t stand in the way of plans to vote on different versions of the legislation.

“These votes, frankly, are a lot tougher for them than they are for us. They are squeezed in both directions,” Senate Minority Leader Charles Schumer, D-N.Y., told reporters.

Sen. Dick Durbin, D-Ill., the party’s top vote-counter, acknowledged that some Democrats might support GOP-written amendments to the bill that have bipartisan support. But he said Democrats will focus mostly on process over policy, and keep pushing Republicans to return the legislation to committee and proceed with regular procedure. There have been bipartisan complaints that the legislation was drafted – by McConnell and a handful of leaders – without enough transparency.

Recognizing their lack of leverage in the chamber, Senate Democrats decried Republicans’ policies and procedural approach in a rally with supporters outside the Capitol. “How about we fill the streets outside every Republican office in America?” said Sen. Jeff Merkley, D-Ore.

Several patient-advocate organizations and progressive groups decried the vote, warning that it could open the door to rollbacks in the expanded coverage the ACA has provided through new benefits requirements and greater federal support for insurance coverage.

“Republican leaders are using undemocratic and unprecedented means to rob coverage and critical services from millions of women, sending them back to a time when Women’s Health Care Services were not considered essential,” Nancy Northup, president and chief executive of the Center for Reproductive Rights, said in a statement.

Meanwhile, Nathan Nascimento, vice president of the conservative group Freedom Partners, urged senators to use the votes to partly repeal the law and then keep pushing for full repeal. “And then use the next available opportunity to keep their promise by repealing the rest of Obamacare, including its costly regulations and choice-stifling mandates,” he said.

The Washington Post’s Amy Goldstein, Ed O’Keefe, David Weigel and Paige Winfield Cunningham contributed to this report.