The Senate is considering holding a vote on adding an ObamaCare stabilization measure into a must-pass government funding bill in order to get lawmakers on record on the issue.

The ObamaCare proposal is in serious jeopardy amid a dispute between the parties over abortion restrictions in the new funding aimed at lowering ObamaCare premiums.

Sources say the House is not expected to include the health-care measure in its version of a government funding bill set to be released as early as Monday night.

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Sen. Lamar Alexander Andrew (Lamar) Lamar AlexanderMcConnell locks down key GOP votes in Supreme Court fight Alexander backs vote on Trump Supreme Court nominee: What Democrats 'would do if the shoe were on the other foot' Toobin: McConnell engaging in 'greatest act of hypocrisy in American political history' with Ginsburg replacement vote MORE (R-Tenn.) said that if the House does not include his proposal in the government funding bill, then he wants a vote in the Senate on adding the provisions into the package.

If the House does not include the proposal, Alexander said, "another option would be that Senator McConnell could put it in the bill here, we could vote on it, pass it and send it back to the House."

David Popp, a spokesman for Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellOcasio-Cortez to voters: Tell McConnell 'he is playing with fire' with Ginsburg's seat McConnell locks down key GOP votes in Supreme Court fight Video shows NYC subway station renamed after Ruth Bader Ginsburg MORE (R-Ky.), noted that the government funding bill is still being negotiated, but added that McConnell is "open" to a vote in the Senate on adding in the ObamaCare fix.

Some observers say they think a Senate vote would be largely symbolic since there would need to be significant Democratic support for it to pass the chamber. Democrats say the abortion restrictions are a dealbreaker.

Alexander, though, said he wants lawmakers to at least be on record on his proposal to lower premiums, acknowledging that premium increases set to be announced in October are sure to become caught up in midterm campaign messaging.

"My only goal is I want senators and congressmen to have a chance to vote on this," Alexander said. "This is going to be announced on Oct. 1, one month before the election, I want them to be accountable for a vote on an opportunity that we all have to lower rates by 40 percent."

Alexander made the comments after leaving a meeting in McConnell's office on Monday afternoon along with Sen. Susan Collins Susan Margaret CollinsMcConnell locks down key GOP votes in Supreme Court fight Most Americans think winner of election should pick next Supreme Court justice: poll Murkowski: Supreme Court nominee should not be taken up before election MORE (R-Maine), who has worked closely with him on the proposal.

Both Alexander and Collins said they see no reason for Democrats to oppose the bill over the restrictions on federal money going to abortions, known as the Hyde Amendment. They noted those restrictions have been in place since the 1970s.

Democrats, though, say that applying the restrictions to ObamaCare funds would be an expansion of the Hyde Amendment that would prevent funds from going to an insurer if it offered abortion coverage at all.

Collins won a commitment from McConnell to support the ObamaCare fix in exchange for her vote for the tax reform bill last year.