Republicans on their part fear they would take the blame for the ACA's problems now that they control both chambers of Congress and the White House, "And Democrats are eager to stabilize President Barack Obama's signature health care law," Politico writes. "Roughly 25,000 Obamacare customers in 38 states are currently facing danger of having no insurers willing to offer coverage next year, according to the Kaiser Family Foundation. In many other places, Obamacare customers only have one insurance option."

The Washington Post reports that Sen. Lamar Alexander (R-Tenn.), who chairs the Senate Health, Education, Labor and Pensions (HELP) Committee — considered "a bipartisan bright spot" in the Senate — says the failure of the GOP repeal effort "leaves an urgent problem that I am committed to addressing."

Sen. Thomas R. Carper (D-Del.) says Congress needs "to turn the page and stabilize the exchanges." The most immediate priority for a bipartisan bill would be to require the Trump administration to enforce the current individual and employer mandates and fully fund current cost-sharing arrangements.

"The drawn-out health care debate on Capitol Hill has left lawmakers and administration officials with very little time to reassure jittery insurers that the markets created by the ACA will be stable enough for them to offer plans at a reasonable rates, The Post writes. "Under guidelines issued by the Health and Human Services Department, companies must set their final rates by Aug. 16 and states must submit the rates they've approved to federal officials by Sept. 27."

Sen. Amy Klobuchar (D-Minn.) said that fresh bipartisan talks also should include plans to reduce the cost of prescription drugs, according to The Post.

Other Senate committees are also starting to work on a bipartisan fix, according to The Hill. Sen. Ron Johnson (R-Wis.), chair of the Senate Homeland Security and Governmental Affairs Committee, says he's already talked to his ranking member, "and we're already starting to lay out a hearing schedule, just laying out basic problem-solving process."

Congress needs to agree on three main objectives, according to The Hill: the need to have bipartisan committee work, a desire to stabilize insurance markets and calls for administration action to change the health care law.

Sen. Mike Rounds (R-S.D.), a former insurance executive, worries that it's too late to appropriate the ACA'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," Round says. "We don't have — it'll be very difficult to get it done in time to impact rates next year. What I'm really worried about is I'm afraid the prices will probably rise well over 20 percent."

Sen. Bill Cassidy (R-La.), one of the principal GOP proponents of a bipartisan fix, concedes there's a possibility that President Trump could sabotage any efforts via executive actions. For example, the Trump administration could end the cost-sharing reduction payments, as well as stop enforcing the individual mandate, "a move experts warn could cause the insurance markets to collapse," Politico writes.

Sen. Roy Blunt (R-Mo.) says he hopes 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 ACA 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 says.

Advocacy groups are wasting no time weighing in on what they would like to see in any bipartisan fix.

"We hope that efforts to permanently repeal the excise tax and to enhance health accounts continue," Steve Wojcik, vice president, public policy at the National Business Group on Health, writes in an emailed statement. "There is broad bipartisan support to eliminate the excise tax, which will raise costs for employers and the 175 million people covered by employer plans if it takes effect. Making it easier to use and save more in health accounts will help millions of Americans pay for out-of-pocket expenses."

Neera Tanden, president and chief executive of the Center for American Progress, and Topher Spiro, the group's vice president of health policy, writes in The Washington Post that they have already proposed three solutions to stabilize insurance markets: Congress should guarantee continued payments of ACA subsidies, make sure that insurers are reimbursed for covering high-cost patients who need more expensive medical treatment, and fill insurance gaps in areas of the country that have one or no insurers.

Lawmakers could do this by either exempting insurers in those areas from paying the health-insurance tax, or offer a public option in the form of a guaranteed choice plan — such as the Federal Employees Health Benefits Program — in communities without sufficient competition, particularly rural areas.

"Republican senators such as Bob Corker and Lamar Alexander of Tennessee and Democratic Sen. Claire McCaskill of Missouri have previously supported the idea of filling insurance gaps for these underserved counties," the two write.

"It's time to stop using health care as a political weapon," they write. "With both parties invested in the solution, they would have an incentive to make it work. The time for bipartisan action should be now."