Sens. Patty Murray (D-Wash.) and Lamar Alexander (R-Tenn.) speak before the start of a hearing in Washington on Oct. 19. (Zach Gibson/Bloomberg)

Democrats pressed Thursday to advance a bipartisan bill that would preserve subsidies for low-income Americans under the ­Affordable Care Act amid a new show of cooperation, even as Republican leaders suggested that they would need greater concessions before bringing it up for a vote.

President Trump, meanwhile, suggested that he was "open" to authorizing payments to insurers that help offset out-of-pocket health costs in the short term — but had not given up his goal of repealing the ACA.

Senate Health, Education, Labor and Pensions Committee Chairman Lamar Alexander (R-Tenn.) and ranking Democratic member Patty Murray (Wash.), who wrote the new health-care package, said that there are 12 Republican and 12 Democratic co-sponsors for their measure. It would continue the cost-sharing reduction payments, known as CSRs, in exchange for giving states greater latitude to regulate health coverage.

Many conservative Republicans, including congressional leaders, have expressed skepticism about passing legislation that would roll back the ACA in a meaningful way. Although the bill does make it easier for states to obtain federal waivers to change the way their markets operate and allows ACA consumers ages 30 and older to buy catastrophic health plans, it preserves the law's core mandates.

Speaking on the floor Wednesday, Alexander said those conservatives were ignoring the "chaos" that could ensue if the federal government did not provide the cost-sharing reduction payments that Trump cut off this month.

"What's conservative about unaffordable premiums?" he asked.

Even as Alexander and Murray announced their sponsors — which included conservatives and liberals, as well as centrists from both parties —, a top Republican argued that the plan had to undergo changes and win the clear support of Trump before it could succeed.

"It takes the president's support, would be the first thing it would take," said Senate Majority Whip John Cornyn (R-Tex.). "I know they've got bipartisan co-sponsors. Senator Alexander is a very methodical, very thoughtful guy. He understands that there are going to need to be changes to be — before [the bill is] going to get a critical mass of support."

Trump called Alexander twice Wednesday, the senator said, and each time encouraged him to continue working on a deal.

The president told reporters Thursday that although he prefers providing federal health funding in a block grant to states, he is open to a different approach for a finite period.

"We will probably like a very short-term solution until we hit the block grants, until that all kicks in," he said. "And if they can do something like that, I'm open to it, but I don't want it to be at the expense of the people. I want to take care of our people; I don't want to take care of our insurance companies."

The president has repeatedly decried the idea of paying money to insurers, which is the way cost-sharing payments are distributed.

Sens. Lindsey O. Graham (R-S.C.) and Bill Cassidy (R-La.), whose own ACA overhaul bill faltered late last month, signed on to the new bill and have been working with Sen. Ron Johnson (R-Wis.) to broker a compromise that would address the concerns of the White House and House Republicans. Johnson was "leading the effort to find a bridge," Graham said.

Murray said she was confident that Congress would ultimately pass the measure because Americans are beginning to grasp that the impasse in Washington has translated into higher insurance rates for 2018. "Here's what's really at stake," she said. "Patients and families across the country are looking ahead to next year, and they are realizing they are about to pay the price for the uncertainty and partisanship we've seen — especially from the Trump administration — on health care over the last nine months."

The additional sponsors include Republicans Mike Rounds (S.D.), John McCain (Ariz.), Susan Collins (Maine), Joni Ernst (Iowa), Lisa Murkowski (Alaska), Charles E. Grassley (Iowa), Johnny Isakson (Ga.), Richard Burr (N.C.) and Bob Corker (Tenn.). The Democrats are Angus King (Maine), Jeanne Shaheen (N.H.), Joe Donnelly (Ind.), Amy Klobuchar (Minn.), Heidi Heitkamp (N.D.), Al Franken (Minn.), Joe Manchin III (W.Va.), Thomas R. Carper (Del.), Tammy Baldwin (Wis.), Claire McCaskill (Mo.), and Maggie Hassan (N.H.). King is an independent but caucuses with the Democrats.

Senate Minority Leader Charles E. Schumer (D-N.Y.) urged Senate Majority Leader Mitch McConnell (R-Ky.) to bring the proposal to the floor for debate and a vote.

"Since every Democrat, I believe, will support it, it has 60 votes," Schumer told reporters. "I'd urge Senator McConnell to put it right on the floor."

A broad coalition of health groups, including the American Heart Association and the American Diabetes Association, have endorsed the bill, along with a bipartisan coalition of 10 governors.

The fate of the cost-sharing payments may be determined by litigation before Congress acts. A federal judge has scheduled a hearing Monday on a motion by 18 states and the District of Columbia, which are seeking a temporary restraining order to force the Trump administration to continue funding the subsidy.

John Wagner contributed to this report.