Senators who walked off the floor around 2 a.m. Friday after the stunning defeat of the latest GOP ObamaCare repeal effort face tough questions on how to move forward.

GOP leaders sounded pessimistic notes that the failure would lead to compromise or bipartisan work on healthcare, though some members said they hoped it would spur leaders to start a more formal process of committee work after months on Senate bills being drawn up behind closed doors.

“We're not adverse to that,” said Sen. John Thune John Randolph ThuneGraham: GOP will confirm Trump's Supreme Court nominee before the election Tumultuous court battle upends fight for Senate What Senate Republicans have said about election-year Supreme Court vacancies MORE (S.D.), the No. 3 Senate Republican. “I just don’t have high hopes that we're going to get anything that really solves the problems that we think exist with ObamaCare today."

From the get-go, some senators have called for a bipartisan process, frustrated with how leadership crafted the repeal-and-replace bill behind closed doors.

Sen. Ron Johnson Ronald (Ron) Harold JohnsonThis week: Supreme Court fight over Ginsburg's seat upends Congress's agenda GOP set to release controversial Biden report Democrats fear Russia interference could spoil bid to retake Senate MORE (R-Wis.) has been chief among them.

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“I've already talked to my ranking member, and we're already starting to lay out a hearing schedule, just laying out basic problem-solving process,” said Johnson, the chairman of the Senate Homeland Security and Governmental Affairs Committee.

In a speech on the Senate floor, Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellGraham: GOP will confirm Trump's Supreme Court nominee before the election Trump puts Supreme Court fight at center of Ohio rally The Memo: Dems face balancing act on SCOTUS fight MORE (R-Ky.) at times looked emotional as he called the defeat “clearly a disappointing moment” and said “it’s time to move on.”

He also challenged Democrats, who themselves are likely not unified on an approach to healthcare, to find a solution.

“So now I think it’s appropriate to ask what are their ideas,” McConnell said. “It would be interesting to see what they suggest as the way forward.”

Three main points quickly emerged after the GOP's seven-year effort to kill off ObamaCare seemed to die a final death: the need to have bipartisan committee work, a desire to stabilize insurance markets and calls for administration action to change the healthcare law.

Sen. Lisa Murkowski Lisa Ann MurkowskiGraham: GOP will confirm Trump's Supreme Court nominee before the election Gardner signals support for taking up Supreme Court nominee this year Tumultuous court battle upends fight for Senate MORE (R-Alaska), one of three Republicans to vote against the so-called skinny bill, said she talked to Sen. Lamar Alexander Andrew (Lamar) Lamar AlexanderGraham: GOP will confirm Trump's Supreme Court nominee before the election The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE (R-Tenn.), the chairman of the Senate Health Committee, on the floor, and he is already putting panel staff to work.

Thune also said Alexander and his committee's ranking Democrat, Sen. Patty Murray Patricia (Patty) Lynn MurrayTrump health officials grilled over reports of politics in COVID-19 response CDC director pushes back on Caputo claim of 'resistance unit' at agency The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (Wash.), could work on fixes to the healthcare system in committee.

Alexander has previously said that the Senate Health Committee will hold hearings in the next few weeks to explore stabilizing the individual market — and that the hearings would happen “however the votes come out on the Senate healthcare bill.”

He said in a statement early Friday morning that it was urgent something be done to help the individual market.

“Tennessee's state insurance commissioner says our individual insurance market is very near collapse,” Alexander said.

“Unless Congress acts, many of the 350,000 Tennesseans who buy health insurance in that market — songwriters, farmers, the self-employed — face the real prospect of having zero options to buy insurance in 2018 and 2019.”

Democrats are split on an approach, with some supporting a single-payer, government-funded system.

In a statement early Friday morning, Murray said she looks forward to bipartisan hearings and more discussions.

Healthcare has been contentious and bitterly partisan for more than seven years, and relationships would have to be repaired if the two parties are to work together.

“I think that's part of the challenge because it has been such a polarizing issue for so long,” Thune said, “and part of that is just fundamentally different approaches and directions and visions for what you want to see happen.”

Johnson offered his suggestions: “Find the areas of agreement, and it starts with: agree on the facts, lay out the reality, do the root cause analysis. To me, that is the problem-solving process.”

But Republicans will have to act quickly if they want to stabilize the markets. Insurers must make decisions by September on whether they will leave the ObamaCare exchanges or increase premiums.

Sen. Mike Rounds (R-S.D.), a former insurance executive, worried that it’s too late to appropriate ObamaCare’s cost-sharing reduction payments, which reimburse insurers for giving discounted deductibles and copays to low-income customers.

“We can always start, the problem is the timing. We don’t have — it’ll be very difficult to get it done in time to impact rates next year,” he said.

“What I’m really worried about is I’m afraid the prices will probably rise well over 20 percent.”

In the meantime, President Trump and his administration face decisions on how to handle the healthcare law. And it doesn’t look like he’s going to do much to prop up the law’s exchanges.

“As I said from the beginning, let ObamaCare implode, then deal. Watch!” Trump tweeted after the bill failed.

Sen. Bill Cassidy (R-La.) admitted that’s a possibility.

“The wildcard is what the president does,” he said.

“Obviously the president, through executive action, can make things ever more difficult. And that’s a possibility.”

For example, the Trump administration could end ObamaCare’s cost-sharing reduction payments.

Insurers have been begging for long-term certainty over these payments, which the administration has been making on a month-to-month basis.

The Trump administration could also decide to stop enforcing the individual mandate, a move experts warn could cause the insurance markets to collapse. The mandate is designed to bring in healthy enrollees to balance out the sick ones. But if healthy people have no incentive to buy insurance, only the sickest will, sending premiums soaring.

It’s also unclear if the Trump administration will continue advertising and outreach for ObamaCare, which is intended to promote exchange signups. The White House pulled $5 million in advertising during the last open enrollment cycle and also has produced ads disparaging the law.

Sen. Roy Blunt Roy Dean BluntThis week: Supreme Court fight over Ginsburg's seat upends Congress's agenda McConnell locks down key GOP votes in Supreme Court fight Murkowski: Supreme Court nominee should not be taken up before election MORE (R-Mo.) hoped that Health and Human Services Secretary Tom Price could use his authority to make beneficial changes to the law. Price has previously talked about some market stability measures and helping states apply for waivers for certain ObamaCare provisions.

“I think this ends this discussion for a little while and Tom Price is going to continue to look at all of the 1,400 places in the bill that his department is responsible for defining how this might work better,” Blunt said.

Nathaniel Weixel and Jordain Carney contributed.