Sen. Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.) is opening the door to helping GOP leadership get a healthcare bill over a key procedural hurdle.

The Kentucky Republican said on Thursday that he would support the motion to proceed to the House-passed healthcare bill, which is being used as a vehicle for any action, if he could get a deal on amendments.

"If they want my vote, they have to at least agree that we're going to at least have a vote on clean repeal," Paul told reporters.

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The Kentucky Republican floated that Senate leadership should guarantee votes on some of the caucus's most prominent healthcare proposals — including repeal-only, repeal-and-replace and a bill created by Sens. Bill Cassidy (R-La.) and 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) — as a way to get him on board.

"I think they're pretty equal in support. Let's do a random selection. Let's have three or four of them, put them in random order, the first day, equal billing. I think that's a compromise. I'm willing to get on the bill," he said.

Senators are expected to hold a procedural vote on Tuesday.

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.) will need the support of at least 50 GOP senators to take up the House bill and let senators offer amendments, including clean repeal, the Better Care Reconciliation Act or other proposals.

Three GOP senators have said they would not take up the bill if it's to proceed to a repeal-only proposal. Paul and GOP Sen. Susan Collins (R-Maine) do not support the Senate GOP repeal-and-replace plan.

Paul is widely viewed as one of the most entrenched "no" votes within the GOP caucus on healthcare. If leadership is able to win him over, it could bolster their chances to at least debate — if not ultimately pass — healthcare legislation.

McConnell's math is even narrower with Sen. John McCain John Sidney McCainMomentum growing among Republicans for Supreme Court vote before Election Day McConnell urges GOP senators to 'keep your powder dry' on Supreme Court vacancy McSally says current Senate should vote on Trump nominee MORE (R-Ariz.), who announced on Wednesday night that he had been diagnosed with brain cancer, out of Washington. It's unclear when he will return.

With McCain absent and all other 99 senators voting, McConnell can only afford to lose one GOP senator.

Paul stressed that he was not yet on board with voting "yes" on the initial hurdle, adding that there has been "resistance" to his idea.

If the Senate is able to take up the House bill any senator will be able to offer an amendment under an hours-long "vote-a-rama," but Paul said he wanted a guarantee his amendment wouldn't get buried in a "four in the morning" vote.

"Up front we have a vote on clean repeal, and maybe BRCA, and maybe Collins-Cassidy. I think the major proposals could be put at the very front. We debate them on the first day," he said.

GOP leadership signaled that they might not know what the ultimate outcome will be, repeal-only or repeal-and-replace, until after they get on the House bill.

"Asking what the first amendment is going to be actually misses the point, because anybody that's got a better idea can offer that and nobody can stop them," said Sen. John Cornyn John CornynCalls grow for Biden to expand election map in final sprint Bipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection MORE (R-Texas).