Sens. Lamar Alexander Andrew (Lamar) Lamar AlexanderChamber of Commerce endorses McSally for reelection Trump health officials grilled over reports of politics in COVID-19 response Now is the time to renew our focus on students and their futures MORE (R-Tenn.) and 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 (D-Wash.) met Wednesday to discuss the path forward for their bipartisan legislation aimed at stabilizing ObamaCare, aides in both parties said.

The legislation’s future has been thrown into question after it was punted at the end of last month. Alexander is now pushing for the legislation to be included in a government funding package when a long-term deal on that measure is reached.

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Murray and other Democrats, though, want significant changes to the bill, saying that it needs to be redone now that Republicans have destabilized health insurance markets by repealing ObamaCare’s individual mandate in the tax-reform bill last month.

Democrats have not yet said what changes they are looking for.

But Alexander told reporters on Wednesday that the bill will remain “fundamentally what was agreed to.”

“It's fundamentally what was agreed to,” he said. “It's what we recommended, plus the Collins-Nelson risk pool."

Alexander was referring to a companion bill from Sens. Susan Collins Susan Margaret CollinsSenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (R-Maine) and Bill Nelson Clarence (Bill) William NelsonDemocrats sound alarm on possible election chaos Trump, facing trouble in Florida, goes all in NASA names DC headquarters after agency's first Black female engineer Mary W. Jackson MORE (D-Fla.) that provides funding known as reinsurance aimed at bringing down premiums.

Collins is a key player on the issue, since Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE (R-Ky.) gave her a commitment to support passage of the two ObamaCare fixes in exchange for her vote for tax reform. Consideration of the two bills was originally supposed to occur before the end of 2017, but has now been put off.

The Alexander-Murray bill funds key payments to insurers known as cost-sharing reductions that President Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE cancelled last year. But Democrats say that measure needs to be rethought now that many experts say cancelling the payments has actually helped the law through a quirk that led to increased subsidies that help people afford coverage.