Bipartisan health bill offers hope for compromise but faces hurdles

— -- Today on the Senate floor, Sen. Lamar Alexander, R-Tenn. and Sen. Patty Murray, D-Wash., introduced their bipartisan health care bill that aims to fund federal subsidies for two years and stabilize individual insurance markets.

After working on a bipartisan, short-term fix to health care for months, Alexander and Murray presented their legislation and named a list of 22 other Democratic and Republican co-sponsors that could help propel their bill forward. Among the supporters are Sen. John McCain, R-Ariz., Sen. Lisa Murkowski, R-Alaska, and Sen. Susan Collins, R-Maine -- the three senators who sunk the Republican Party's effort to repeal and replace Obamacare this summer.

With the added support for the proposal, said Alexander, it “sounds like something that might actually become law before the end of the year.”

The bill has gained the support of 10 bipartisan governors, the America's Health Insurance Plans, the American Medical Association, and a group of 29 non-partisan patient, consumer, and health care groups.

But while Alexander and Murray have sent a clear signal they intend to continue working on their bill, it is still in the hands of Senate Majority Leader Mitch McConnell, R-Ky., to bring the bill to the floor for votes, and House Speaker Paul Ryan, R-Wis., has said he only intends to support repealing and replacing Obamacare.

President Donald Trump has sent mixed signals about whether or not he can support the legislation as well.

Alexander said that over the course of 10 days, he’s taken four phone calls from the president to discuss cost-sharing reductions.

“The president encouraged me, and I said Mr. President, thank you for your leadership, thank you for four calls in ten days on this, and Sen. Murray and I hope you will consider it and strengthen it if you would like to. And he said he would,” Alexander said.

Trump has expressed his concerns about cost-sharing reductions benefitting insurance companies.

“I have great respect, as you know, for both of the senators you mentioned. And if they can come up with a short-term solution. What I did say is I don't want the insurance companies making any more money than they have to, because you look at the stock prices of the insurance prices from the time of the creation of Obamacare,” said Trump today in the Oval Office.

But Murray and Alexander said they both worked hard to make sure consumers -- and not insurance companies -- benefit.

“The one issue we did not disagree on but we worked the hardest on, and had the most discussion on, was how we make sure we have the language in place in this that consumers benefit and it is not a bailout for insurers,” said Murray.

Despite some mixed signals from Trump and no commitment from McConnell for a vote, Murray and Alexander are intent on moving their bill forward. The two have been working for months on the Senate Committee on Health, Education, Labor, and Pensions to fix a small, but stressed, part of the health care marketplace. The bill aims to benefit the premiums of about 6 percent of the population, or 18 million Americans who go into the individual markets to buy health care coverage. Most Americans are insured by the government or their employers.

But the individual marketplace isn’t the only part of the Affordable Care Act the Alexander-Murray bill hopes to change. With Open Enrollment for Obamacare marketplaces less than two weeks away, the bill also hopes to reinstate much of the funding that was stripped by the federal government this year to help people enroll in health insurance plans.

In the midst of all this, other senators have been working to promote their own health care plans. Sens. Lindsey Graham, R-S.C., and Bill Cassidy, R-La., whose health care reform bill was the latest to fail, just announced that they are working on an alternative measure to stabilize markets to the Alexander-Murray bill -- this despite the fact that both Graham and Cassidy are co-sponsors of the Alexander-Murray bill.

Graham and Cassidy say that they want their bill to include "more flexibility provisions." The Alexander-Murray plan gives states more flexibility to receive waivers to create their own programs and opens up catastrophic plans to people over the age of 30.

“Without a stabilization package, the market will collapse and advance premium tax credits will spike," they said in a joint statement. "This would increase the costs to the American taxpayer.”

This week, Sen. Tim Kaine, D-Va., and Sen. Michael Bennet, D-Colo., also introduced their own health care bill, known as Medicare-X, which allows for a public option on Obamacare exchanges that they hope is a moderate Democrat response to the growing support for Vermont Sen. Bernie Sanders' "Medicare for all" bill

For now, Alexander and Murray are committed to finding ways to provide consumers short-term relief.

Alexander gave a stern warning to his Senate colleagues who have been uncertain about funding the cost-sharing reduction payments: “Unless they're replaced with something else temporarily, there will be chaos in this country and millions of Americans will be hurt.”

ABC News' MaryAlice Parks contributed to this report.