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The hangup remains that many Republican senators are dubious of any agreement to stabilize Obamacare

They've spent years railing against the program and pledged to eliminate it

(CNN) —  

Republicans and Democrats could be on the verge of a bipartisan fix to stabilize Obamacare markets, but it may not matter if enough GOP lawmakers cannot get behind it.

Senate health committee Chairman Lamar Alexander, R- Tennessee, pulled the plug on bipartisan talks to fix Obamacare last week to focus on the latest GOP effort to repeal the Affordable Care Act. But with that bill now shelved, he is back at the negotiating table with Democrat Patty Murray.

The main issues: guaranteeing the payment of a key set of Obamacare subsidies at least through next year, which Democrats want, and providing more flexibility for states to amend Obamacare’s regulations, which is critical for Republicans.

“Work in the health committee showed there’s a lot of common ground around ways to strengthen markets and bring down premiums in the near term, and now that Republicans are back at the table, Senator Murray is very hopeful an agreement can be finalized soon,” a Murray aide said.

Among the points the Democrats have agreed to is allowing more Obamacare enrollees to sign up for copper plans, which cover fewer benefits but have lower premiums, and expediting the approval process for states to receive Obamacare waivers, a Senate Democratic aide said.

Alexander struck a more cautious tone. The hangup remains that many Republican senators are dubious of any agreement to stabilize Obamacare, a program they’ve spent years railing against and pledged to eliminate.

“We’re still talking. It’s not a matter of just whether Sen. Murray and I agree. It’s a matter of whether we can find a consensus among Republicans and Democrats that we believe can be enacted into a result,” Alexander said Wednesday. “So she and I might come to an agreement tonight but that wouldn’t do the job. We need to get a significant number of Democrats and a significant number of Republicans, hand it to Sen. (Mitch) McConnell and (Chuck) Schumer, and then we’ve got a matter of eventually persuading the entire Senate, the House of Representatives and the President, so we’re taking it a step at a time.”

Sen. John Barrasso, a Republican from Wyoming and a member of GOP leadership, said Wednesday that “I want to see the states get a lot more flexibility before it’s anything I’m willing to support.”

Also, a deal likely would have had more impact had it come earlier this month. Wednesday was the deadline for insurers to sign contracts locking them into participating for 2018. Also, they have already finalized their premiums for next year, with many insurers hiking rates because they don’t know whether the Trump administration will continue paying the cost-sharing subsidies.