CNN  — 

Conservatives are pushing Senate Majority Leader Mitch McConnell behind the scenes to consider moving to fill the Supreme Court vacancy left by Justice Ruth Bader Ginsburg before the November election, potentially leaving the conference divided over what timeline is best.

Following Ginsburg’s death on Friday, McConnell vowed that whomever President Donald Trump nominates to replace the liberal justice will get a vote on the Senate floor, signaling a historic fight in Congress over one of the most polarizing issues in American politics.

His statement did not make clear the exact timing of such a fight – in particular how much of it would happen ahead of or after Election Day.

Ultimately, it will be McConnell’s decision and not one that he will make without hearing from members in the coming hours and days.

Republican aides across the ideological spectrum point to the importance of Tuesday’s conference lunch on Capitol Hill. It will be the first opportunity members will have to hear from their colleagues in-person about the potential political costs of waiting versus acting now.

For conservatives in the conference, the thinking is that waiting until after the election leaves too many things to chance: the outcome of the election for one and the risk that some moderates may deem it inappropriate to vote on Trump’s nominee in the lame duck session if he loses in November. Conservatives also worry that the Supreme Court may potentially play a pivotal role in the election results if the contest is disputed.

Another factor is that Arizona election experts have argued that if Democratic Senate candidate Mark Kelly were to win his race against Sen. Martha McSally, he could potentially be seated at the end of November – giving McConnell less room for error.

Senate Republicans only need a simple majority of 51 votes to confirm a new justice once one is formally nominated and there are 53 GOP senators currently. McConnell can only afford to lose three Republicans.

If Kelly wins a November 3 special election against McSally, he could be sworn-in as soon as November 30, according to The Arizona Republic, meaning the balance of power in the Senate would shift from the current 53 Republicans and 47 Democrats to 52 Republicans and 48 Democrats.

Republicans have the power now and as the old saying goes: when you have the votes, you vote.

“Why wait?” one Republican aide asked when pushed on the timeline.

“The court is one of the signature accomplishments of the President and this Senate so we need to do all that we can right now,” another GOP aide told CNN.

Sen. Ted Cruz, a Republican from Texas, told Fox News just hours after the news of Ginsburg’s death broke Friday, “I believe that the President should next week nominee a successor to the court, and I think it is critical that the Senate takes up and confirms that successor before Election Day.”

The political Rubik’s cube is infinitely complicated for McConnell, however, who must balance the wishes of conservatives looking to move rapidly with the concerns of some moderate Republicans, who would have to face voters weeks or even days after a contentious Supreme Court fight.

But Republican aides warn that the calculus won’t be the same for every member up for reelection.

For some, motivating their conservative base around a Supreme Court fight may help solidify their support.

Already, Sen. Thom Tillis, a Republican from North Carolina up in November, has made it clear he stands ready to support Trump’s nominee – though none has been named yet.

“There is a clear choice on the future of the Supreme Court between the well-qualified and conservative jurist President Trump will nominate and I will support, and the liberal activist Joe Biden will nominate and Cal Cunningham will support, who will legislate radical, left-wing policies from the bench,” Tillis said.

Trump wrote on Twitter Saturday that Republicans have an “obligation” to fill Ginsburg’s vacant seat on the Supreme Court “without delay.”

CNN’s Veronica Stracqualursi contributed to this story.