Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellRepublicans seem set to win the midterms — unless they defeat themselves Graham emerges as go-to ally for Biden's judicial picks Five reasons for Biden, GOP to be thankful this season MORE (R-Ky.) is warning his colleagues to not block the chamber from taking up a bill to repeal and replace ObamaCare as leadership struggles to shore up support for the legislation. 

"I'm sure members will have other good ideas ... and I hope they will offer them. ... But if the Senate is prevented from even proceeding to the bill, none of us will have an opportunity — not Republicans, not Democrats, not anyone," McConnell said from the Senate floor Wednesday. 

McConnell's comments come as at least 10 GOP senators have publicly voiced opposition to the current version of the healthcare legislation. Leadership had wanted to vote in late June but had to delay the measure because of resistance from both moderates and conservatives. 

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GOP leaders are expected to unveil an updated bill on Thursday, potentially paving the way for a vote on the legislation next week. A crucial new analysis from the Congressional Budget Office is expected to be released on Monday.

McConnell will need at least 50 of the 52 GOP senators to vote to allow the bill to be bought up, assuming Vice President Pence casts the tiebreaking vote, but could face an uphill battle in winning over enough support.

Sen. Rand PaulRandal (Rand) Howard PaulFauci overwhelmed by calls after journal published mistake over beagle experiments McConnell looks for way out of debt ceiling box Senators make bipartisan push to block 0M weapons sale to Saudis MORE (R-Ky.) told reporters during a conference call Wednesday that he was still opposed to the Senate's legislation and thought it was moving in the wrong direction.

"Doesn’t sound much like repeal to me. One might even argue it’s worse than ObamaCare-lite because it actually creates a giant superfund to bail out the insurance companies — something even the Democrats feared to do," he wrote in a Breitbart News op-ed

Sen. Susan CollinsSusan Margaret CollinsGraham emerges as go-to ally for Biden's judicial picks On The Money — Biden sticks with Powell despite pressure Senators call for Smithsonian Latino, women's museums to be built on National Mall MORE (R-Maine) told reporters before a closed-door conference lunch on Tuesday where senators were updated on the bill that she needed a "complete overhaul" to support the legislation. 

Sen. Lisa MurkowskiLisa Ann MurkowskiGraham emerges as go-to ally for Biden's judicial picks Man charged with threatening Alaska senators pleads not guilty Two women could lead a powerful Senate spending panel for first time in history MORE (R-Alaska), another key holdout, said after the lunch that there were no changes made that address her concerns.

If McConnell gets the votes to proceed on the Senate's legislation, lawmakers will still have 20 hours of debate on the bill in addition to a freewheeling "vote-a-rama"—a marathon session where any senator can introduce an amendment vote. 

McConnell added on Wednesday that senators, including Democrats, will have a chance for a "robust debate and a robust amendment process." 

"I hope they'll offer more than just a Band-Aid. I hope they'll offer more than just a $32 trillion dollar re-up of a failed idea. But whatever they'd like to propose, I hope they'll take the chance to open debate and advance the legislation process for every senator, for every American," he said.