“I think it’s going to be very difficult” for Republicans to reach agreement on a bill this week, said Senator Susan Collins, Republican of Maine. But, she added, “you never know.”
Senator John McCain, Republican of Arizona, was even more skeptical. “Pigs could fly,” he said.
Republicans have talked for months about possible ways to repair the Affordable Care Act, although they would clearly prefer the wholesale replacement they have long promised.
Senator Lamar Alexander, Republican of Tennessee and the chairman of the Senate health committee, has said he would like to draft legislation geared toward stabilizing the marketplaces and providing a temporary continuation of subsidies paid to insurance companies to offset out-of-pocket medical expenses.
Just this week, Ms. Collins, in announcing her opposition to the repeal bill in its current form, said she wanted to work with members of both parties to “fix the flaws” in the Affordable Care Act.
Last month, senators from both parties met privately to hash out health care issues. The Democrats attending the session included Joe Donnelly of Indiana, Heidi Heitkamp of North Dakota and Joe Manchin III of West Virginia. Among the Republicans were Shelley Moore Capito of West Virginia, Bill Cassidy of Louisiana, Lindsey Graham of South Carolina, and Ms. Collins.
Any change to the existing law is likely to need Mr. McConnell’s participation — and Speaker Paul D. Ryan’s consent. Before that happens, an all-Republican push to repeal the health law may have to die a public death.
“At this stage,” said Senator Brian Schatz, Democrat of Hawaii, “there is general agreement among Democrats that it would be premature to meet with Republicans. We have to know that this repeal bill is dead.”
Ms. Capito, an opponent of the Senate repeal bill as it now stands, said on CNN on Wednesday that if the effort to pass a Republican bill failed, “the floodgates would probably open to reach a bipartisan compromise.”
Nearly everyone preaches the virtues of bipartisanship in Congress these days, but on the big issues that define the two parties, few practice it.
For now, party leaders remain bitter foes. Republican leaders say Democrats should have come to them to help undo what Republicans say is the damage caused by the law that Democrats adopted in 2010 at great political cost.
“It’s unfortunate that our Democratic colleagues refused to work with us in a serious way to comprehensively address Obamacare’s failures,” Mr. McConnell, the Senate bill’s chief author, said Wednesday on the Senate floor.
Credit Eric Thayer for The New York Times
And Democrats are using the prospect of bipartisanship as something of a cudgel, baiting Republicans to come to them, but demanding a price for entry: Keep the Affordable Care Act largely intact.
On Wednesday, Senator Chuck Schumer of New York, the Democratic leader, reminded his colleagues of the daylong gathering in 2010 at Blair House, across the street from the White House, where Mr. Obama discussed health care specifics with members of both parties shortly before passage of the Affordable Care Act.
“President Trump, I challenge you to invite us — all 100 of us, Republican and Democrat — to Blair House to discuss a new bipartisan way forward on health care in front of all the American people,” Mr. Schumer said. “It would focus about what you, Mr. President, have talked about in your campaign: lower costs, better health care, covering ‘everybody’ — not on tax cuts for the rich, not on slashing Medicaid.”
Mr. Trump predicted on Wednesday that “a great, great surprise” would emerge from the Republican health care talks, and he did not take the bait from Mr. Schumer.
“He’s done a lot of talking, bad talking, and he just doesn’t seem like a serious person,” the president said.
Money is often a lubricant for legislation, and because the Senate health bill includes about $200 billion more in deficit reduction over 10 years than the House version, Mr. McConnell has billions of dollars that he could use to address concerns expressed by members of his caucus. Various Republican senators are seeking funds to combat the nation’s opioid epidemic, stabilize health insurance markets, help older Americans pay for health coverage and slow the pace of planned cutbacks to Medicaid.
But pouring more money into the bill to please some senators could antagonize others.
Some of the Senate’s most conservative members have radically different priorities. In a letter to Mr. McConnell, outlining changes he wanted to see, Senator Rand Paul, Republican of Kentucky, complained that the legislation contained $136 billion in assistance for insurers — what he called “insurance company bailouts.”
Another conservative, Senator Mike Lee of Utah, wants to give states more latitude to opt out of federal insurance regulations, so that insurers could charge higher premiums for people based on their health status. But making such a change risks inflaming Republicans who want to keep protections for people with pre-existing medical conditions, a key difference between the Senate bill and the one passed by the House last month.
The deep divisions could elevate Mr. McConnell’s bipartisan fallback from a political threat leveled to get his troops in line to a legislative reality.
While Mr. Trump has blustered about letting the Affordable Care Act “crash and burn,” senators from both parties want to protect consumers who would be the victims if insurance markets collapse in any states. Senior Republicans in the House and Senate have said that Congress should provide money for the so-called cost-sharing subsidies paid to insurers so they can reduce deductibles and other out-of-pocket expenses for low-income people.
The Senate bill would continue the payments through 2019. Mr. Trump has repeatedly threatened to stop the payments to force Democrats to negotiate with him over the Affordable Care Act’s future.
Lawmakers have also offered proposals to address the possibility that consumers in some counties will be left without any insurers offering coverage in their Affordable Care Act marketplace.
Mr. Alexander and Senator Bob Corker, Republican of Tennessee, have proposed allowing consumers in such areas to use federal tax credits to help pay for policies obtained outside the law’s marketplaces.
Democrats and Republicans could also conceivably work together on ways to rein in drug prices and help small businesses with employee health costs.
The overtures have begun — tentatively. Senator Thomas R. Carper, Democrat of Delaware, said that — in emails, text messages, phone calls and occasional meetings — he had been “reaching out to Republicans who would like to find a principled compromise to fix what needs to be fixed in the Affordable Care Act.”
Mr. Carper said on Wednesday that he was trying to “foster an environment in which conversation and collaboration could begin in earnest and continue over the Fourth of July recess.” He has been careful to keep party leaders informed.
“Our leaders are reluctant to have our members, however well intentioned, be lone rangers negotiating on our own,” Mr. Carper said.