Ledyard King and Deirdre Shesgreen, USA TODAY

WASHINGTON — A chance encounter between two senators on an airplane last month in Maine may be the catalyst for a breakthrough on health care reform.

Since that Sunday afternoon meeting at the Bangor Airport, Florida Democrat Bill Nelson and Maine Republican Susan Collins have been talking to each other about ways of finding a solution on an issue that has deeply divided Congress along party lines.

There's no grand bargain in sight, but a low-key dinner the two organized for a bipartisan clutch of senators at a Washington restaurant Wednesday night suggests at least a few lawmakers are trying to find a way out of the partisan gridlock.

That effort took on added significance following the stunning defeat early Friday morning of a Republican bill to do away with some parts of the Affordable Care Act, also known as Obamacare, leaving lawmakers scrambling to decide the best way to move forward on health care reform.

The deciding vote was cast by Arizona Republican Sen. John McCain. He had implored colleagues to reach a bipartisan solution during a stirring floor speech he delivered Tuesday, just days after a brain cancer diagnosis.

The following night, Nelson and Collins hosted the dinner at NoPa Kitchen, an American brasserie steps from the International Spy Museum.

The attendees included key Senate moderates such as Republicans Lisa Murkowski of Alaska and Mike Rounds of South Dakota, and Democrats Joe Donnelly of Indiana, Claire McCaskill of Missouri, Jeanne Shaheen of New Hampshire, Mark Warner of Virginia and Joe Manchin of West Virginia.

Collins and Murkowski joined McCain as the only three Republicans to vote against the bill, which died 51-49.

"It was a good first start and everyone (at the dinner) pretty well knows that the path that we're on is not going to be the ultimate solution," Nelson said Thursday before the bill was killed.

Collins sounded a similar theme following Friday's vote.

"We need to reconsider our approach," she said in a statement posted on her Twitter account. "The ACA is flawed and in portions of the country is near collapse. Rather than engaging in partisan exercises, Republicans and Democrats should work together to address these very serious problems."

Democratic Senate leader Chuck Schumer said he spoke with GOP House Speaker Paul Ryan of Wisconsin on Friday about working together.

“There’s a thirst to do it,” Schumer said. “I just hope the magic moment of John McCain last night has lasting effect and makes us work together in a better way and both sides are to blame for the past.”

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Collins and Nelson, both former insurance commissioners in their states, traded some ideas on the plane ride to Washington during that June flight. Notably, Nelson said, they liked the idea of creating a federal reinsurance fund that would protect the health insurance companies against catastrophe.

Nelson has already introduced a bill to that effect after a Congressional Budget Office analysis concluded it would lower health care premiums 13% in Florida alone.

The more they talked, the more they realized they could work on other aspects of health care reform given the political stalemate between party leaders.

"We said let's do this together," Nelson said. "That led to Susan taking the initiative and inviting everybody that was there to get their ideas."

A reinsurance fund was one ideas that was discussed over dinner, he said. So were ways to address cost-sharing reductions that go to help low-income Americans on the individual health care market pay for coverage. The goal was finding ways to stabilize the health insurance markets, he said.

Manchin touted the reinsurance proposal on the Senate floor Thursday. And McCaskill said lawmakers need to act now to ensure people have someplace they can buy insurance next year.

"We are trying to get the ball moving in a bipartisan way," she said. "So we’re trying to start with a bipartisan group and see if we can’t come up with some ways to stabilize the markets."

The Missouri Democrat said she's hoping to team up with Republicans and "start small and then see if we can grow our number."

When they left the dinner, there was no commitment to meet again as a formal working group. But Nelson said he expects the senators will keep talking.

In his closing comments, Nelson told the group that their roles as moderates who can lead a bipartisan effort would grow if the repeal bill failed,

"There's going to be a vacuum created in which we ought to offer some of these ideas," he said.

USA TODAY reporter Nicole Gaudiano of USA TODAY contributed to this story