Talks between Senate GOP Leader Mitch McConnell and Senate Democratic Leader Chuck Schumer are stalled over a power-sharing agreement on how the Senate will run with 50 senators in each caucus but Vice President Harris giving Democrats a slight edge. 

Such an agreement is not unprecedented. There was a 50-50 Senate at the beginning of the George W. Bush administration, and the two parties put together a deal, which McConnell, R-Ky., and Schumer, D-N.Y., are using as a template for their current talks. 

The deal would govern the number of senators from each party on committees, likely would allow bills to get to the Senate floor even on evenly-split votes in committee and may even give McConnell some rights on the Senate floor that he wouldn't otherwise have if Democrats had 51 senators. 

But the hangup, apparent in public comments from the two senators, is a request from McConnell for assurances that Democrats will not get rid of the legislative filibuster -- the requirement that bills clear a 60-vote procedural hurdle before a final up-or-down vote -- during the upcoming Congress.

Charles Schumer, D-N.Y., stands with Mitch McConnell, R-Ky., as a joint session of the House and Senate convenes to confirm the Electoral College votes cast in November's election, at the Capitol in Washington, Wednesday, Jan. 6, 2021. (Kevin Dietsch/Pool via AP)

Charles Schumer, D-N.Y., stands with Mitch McConnell, R-Ky., as a joint session of the House and Senate convenes to confirm the Electoral College votes cast in November's election, at the Capitol in Washington, Wednesday, Jan. 6, 2021. (Kevin Dietsch/Pool via AP)

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"I’ve been heartened to hear my colleague say he wants the same rules from the 2000s to apply today. Because certainly 20 years ago there was no talk of tearing down long-standing minority rights on legislation," McConnell said in floor remarks Thursday. "The legislative filibuster is a crucial part of the Senate. Leading Democrats like President Biden himself have long defended it."

McConnell then accused Democrats of "liberally" using the filibuster to block GOP legislation during the past six years that Republicans controlled the Senate. Democrats did this on notable occasions in 2020 when Republicans brought up police reform legislation and coronavirus relief bills that Democrats did not think were ambitious enough.

The consequence of the snag is that the Senate will not be able to fully ramp up and handle its normal business, leaving the body in an awkward state of limbo as it begins working through Biden's Cabinet nominations. 

McConnell's floor remarks followed a comment from a McConnell spokesman on Tuesday that during a meeting with Schumer, the GOP leader "expressed his long-held view that the crucial, longstanding, and bipartisan Senate rules concerning the legislative filibuster remain intact." 

But Schumer has called McConnell's request "extraneous" and said Democrats won't go for it. 

US President Joe Biden prepares to sign a series of orders in the Oval Office of the White House in Washington, DC, after being sworn in at the US Capitol on January 20, 2021. The party leaders in the Senate are struggling to come to a power-sharing agreement, something that could handicap its ability to handle Biden's agenda if not handled quickly. (Photo by Jim WATSON / AFP) (Photo by JIM WATSON/AFP via Getty Images)

US President Joe Biden prepares to sign a series of orders in the Oval Office of the White House in Washington, DC, after being sworn in at the US Capitol on January 20, 2021. The party leaders in the Senate are struggling to come to a power-sharing agreement, something that could handicap its ability to handle Biden's agenda if not handled quickly. (Photo by Jim WATSON / AFP) (Photo by JIM WATSON/AFP via Getty Images)

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"We believe, our caucus believes, that the fairest, easiest and most bipartisan way to come to an organizing resolution is to enact the 2001 agreement that Sens. Lott and Daschle came to in bipartisan way back then," he said on Thursday. "We, our caucus is strongly opposed to any extraneous provisions. And so we're going to keep working to try and get a bipartisan deal."

Many Senate Democrats have expressed a desire to get rid of the legislative filibuster, which can be done by a mere 50-plus-one majority if the Senate decides it wants to do that. That is what Democrats did for lower-court nominations during former President Obama's time in office and what Republicans did for Supreme Court nominations during President Trump's term. 

But Republicans and even some Democrats -- specifically Sen. Joe Manchin, D-W.V. -- have said they hope to keep the legislative filibuster intact, citing a desire to preserve the tradition that forces the two sides to compromise to get anything done. 

Schumer said that "everything" would be "on the table" if Republicans confirmed Supreme Court Justice Amy Coney Barrett before the presidential election -- which they did -- but he has not explicitly said he wants to get rid of the filibuster. For the moment, however, he appears to be invested in keeping the option open, even if it would be difficult to convince a reluctant Manchin and perhaps other Democrat senators vote to end the filibuster if he decided to go that way. 

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Meanwhile, Biden's legislative agenda still looms, as does an upcoming impeachment trial for Trump -- something else that McConnell and Schumer will have to come to an agreement on how to run. Biden has asked the Senate to attempt to try to dual-track the impeachment trial and his nominees. 

But Sen. John Cornyn, R-Texas, a close McConnell ally, appeared to throw cold water on the suggestion the Senate would be able to handle business other than impeachment once the House sends the article of impeachment against Trump. 

White House Press Secretary Jen Psaki, according to a tweet by a CNN reporter, said "we are confident the Senate can multi task," regarding the impeachment trial. 

"Nope," Cornyn responded.

A source on a Senate GOP call told Fox News on Thursday that McConnell will offer Schumer his proposal for how he thinks the impeachment trial should be run. It is unclear what exactly will be in the McConnell proposal. 

Fox News' Kelly Phares contributed to this report.