WASHINGTON — Senate Republicans decided Tuesday not to hold a vote on unwinding the Affordable Care Act, effectively preserving the landmark 2010 law for the foreseeable future.

In deciding not to take up the latest proposal, authored by Sens. Lindsey Graham, S.C., and Bill Cassidy, La., their fellow Republicans are abandoning the policy goal that has animated their party for more than seven years.

Top Republicans, however, also indicated they have little interest in shoring up the existing insurance market operating under the 2010 law. Instead, they suggested, the ongoing instability would backfire on Democrats and build momentum for the ACA’s eventual repeal.

“I personally think it’s time for the American people to see what the Democrats have done to them on health care,” said Senate Finance Committee Chairman Orrin Hatch, R-Utah. “They’re going to find they can’t pay for it, they’re going to find that it doesn’t work. … Now that will make it tough on everybody. Maybe that’s what it takes to wise people up.”

Wednesday is the deadline for insurers to sign contracts with the federal government so that they can sell health plans on the ACA marketplaces for 2018. Many companies are hiking these rates by double digits, but they have suggested they would curb such increases if they had assurances that the federal government would provide cost-sharing reduction payments for all of next year.

At the moment, the Trump administration is only covering cost-sharing payments on a month-to-month basis; a White House official confirmed Tuesday that it had made a payment for September. Asked whether the president intended to continue making payments going forward, the aide said officials have not yet decided what to do.

Republicans accepted the reality on Monday evening that the push had sputtered out after Sen. Susan Collins of Maine joined two of her fellow Republicans in formal opposition, but made their final decision during their weekly policy lunch, according to Sen. Jeff Flake, R-Ariz.

The development amounted to a major setback for Senate Majority Leader Mitch McConnell, R-Ky., and President Donald Trump, who spent the past week trying to rally support for a last-ditch attempt to fulfill a long-standing promise before a Senate rule that allows a simple-majority vote on the measure expires at the end of the month. The effort lost much of its steam in the past four days, as it became clear that the new proposal had not resolved the same disagreements that plagued Republicans in a July push.

Lanhee Chen, a research fellow at the Hoover Institution, said in an interview that he had initially hoped the Graham-Cassidy bill would have allowed Republicans to move past their policy divisions on health care.

“I thought at least every Republican, or every conservative, would agree with the idea that when it came to health care, it would make sense to give states the freedom and flexibility to pursue a path that would work best for their residents,” said Chen, who also directs domestic policy studies at Stanford University’s public policy program. “That was a principle I was pretty certain could garner the vast majority of Republicans in the Senate.”

But even that sort of consensus seemed elusive, Chen said, and the fact that Republicans are rushing to pass the bill by the end of the month has produced “a flawed process” that has allowed some critics to sidestep more serious questions, such as the long-term sustainability of the Medicaid program.

Speaking to reporters Tuesday, Trump said he was “disappointed in certain so-called Republicans” who would not back the Graham-Cassidy bill.

The president declined to speculate on whether he wanted lawmakers to actually vote on the measure, saying, “We’ll see what happens.”

“It’s going along and at some point, there will be a repeal and replace,” Trump added. “But we’ll see whether that point is now or whether it will be shortly thereafter.”

Republican leaders could call on Sen. Lamar Alexander, R-Tenn., to revive negotiations with Sen. Patty Murray, D-Wash., on a bipartisan package to stabilize the current insurance marketplaces. The pair had appeared to be reaching an agreement on a plan to guarantee subsidies to help cover out-of-pocket expenses for low-income people in exchange for limited waivers to give states more flexibility in how they spend that money. Those talks stalled when Alexander stepped aside to allow GOP leaders to focus on securing votes for Graham-Cassidy.

On Tuesday Senate Minority Leader Charles Schumer, D-N.Y., reiterated his party’s willingness to work with Republicans to fix the current health-care law — if they abandoned their effort to undo it altogether.

“Once this repeal effort is gone, this repeal and replace, we’re willing — eager — to sit down and come up with bipartisan improvements and do it in the regular order,” Schumer said on the Senate floor.

Some congressional Republicans — such as Rep. Carlos Curbelo, R-Fla., who represents a swing district — echoed that call.

“I think the time for partisan health-care reform has passed, and we should focus on a bipartisan package that provides some regulatory relief, especially on the employer mandate,” Curbelo told reporters, “and also guarantees [cost-sharing subsidies] for the most vulnerable people.”

Many Republicans, however, oppose legislation that would approve the subsidies without reforming the ACA insurance market.

“If you mean by ‘fixing Obamacare’ just dishing more money out to insurance companies, then no,” Senate Majority Whip John Cornyn, R-Texas, told reporters Monday.

At the moment, neither party’s proposal to address the law’s current problems has enough votes to pass. Collins announced Monday that she would not back Graham-Cassidy — which would redistribute federal health-care funding across the country and sharply curb spending on Medicaid — moments after the release of a much-anticipated Congressional Budget Office analysis that forecast “millions” of Americans would lose coverage by 2026.

Two GOP senators — Rand Paul, Ky., and John McCain, Ariz. — already had come out against the measure and were not swayed by a new draft that emerged Monday morning. Republicans hold a 52-to-48 advantage in the Senate; they can lose only two votes from their party and still pass legislation with the help of a tie-breaking vote from Vice President Mike Pence.

A fourth Republican, Sen. Ted Cruz, Texas, indicated through his aides Monday that he would not back the bill in its current form because it would not go far enough in repealing the 2010 law.

Neither last-minute changes over the weekend nor the CBO’s preliminary analysis managed to shift any votes in the bill’s favor. If anything, the report worsened the proposal’s chances by noting that it was impossible to forecast the number of Americans who are likely to lose coverage but that “the direction of the effect is clear.” The report also estimated a $1 trillion loss of federal funding for Medicaid by 2026.

Collins delivered a scathing assessment of the bill in a statement, saying the fourth version that the senators had produced in an effort to win new votes “is as deeply flawed as the previous iterations.”

Speaking to reporters Monday evening, the senator said the administration had lobbied her hard to endorse the bill — and she received a call from Trump before the CBO score was announced.

“I told him that I would go back and look at the numbers one more time, but I was straightforward with him that I was not likely to be a yes vote,” she said, adding that the process had been too hasty. “Last night, a whole new bill came out, which to me epitomizes the problem.”

The legislation’s sponsors had rewritten the bill to deliver more money to Alaska and Maine, in the hopes of winning over Collins and Sen. Lisa Murkowski, Alaska, another key GOP centrist.