Sen. Minority Leader Chuck Schumer, D-N.Y., pushed in a meeting Tuesday for the Senate to adopt the 2001 power-sharing agreement utilized under then-Democratic leader Tom Daschle and Republican leader Trent Lott. 

"Leader Schumer and Leader McConnell had a substantive meeting and made progress on the issues of quickly confirming President-elect Biden’s nominees and conducting a fair impeachment trial," a Schumer spokesperson said in a statement. "On an organizing resolution, Leader Schumer expressed that the fairest, most reasonable and easiest path forward is to adopt the 2001 bipartisan agreement without extraneous changes from either side."

Schumer needs an unhindered agreement with Republicans to quickly confirm Biden's nominees for his Cabinet. 

McConnell, meanwhile, didn't agree to such an agreement without a promise to leave the filibuster intact. "During today’s meeting, Leader McConnell expressed his long-held view that the crucial, longstanding, and bipartisan Senate rules concerning the legislative filibuster remain intact, specifically during the power share for the next two years," a McConnell spokesperson said. 

The last time the Senate was split 50-50, as it will be after Georgia’s Democrat senators-elect take office Wednesday, was in 2001. But at that time, the GOP took the "majority" when Vice President Dick Cheney was the tie-breaking vote. 

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Sens. Lott, R-Miss., and Daschle, D-S.D., shared power such that Lott was the Leader to start Congress. There was equal Republican-Democrat participation on committees, with GOP chairs, and Daschle could call up some bills onto the floor for debate. Bills that receive tie votes in committees advance to the floor. 

Senators would have to agree unanimously to such an agreement. 

Schumer and McConnell remain at an impasse over the legislative filibuster. Currently, most legislation requires 60 votes to end debate. "I believe we also need to address the threats to the legislative filibuster," McConnell wrote in a letter to Republicans on Monday. "As you know, we all resisted the direct calls of President Trump to destroy the Senate by eliminating the legislative filibuster when we controlled the House, the Senate, and the White House."

SENATE CONSIDERING BIDEN NOMINEES TUESDAY, WITH NO ANNOUNCEMENT YET ON HANDLING IMPEACHMENT, OTHER BUSINESS

"We’ve got three things we’ve got to do quickly — impeachment, nomination, Covid," Schumer told reporters of his priorities Tuesday, ahead of his meeting with McConnell. 

McConnell has said he hopes the House will wait until at least Thursday to send the impeachment articles, so as not to overshadow Inauguration Day. House Speaker Nancy Pelosi and top Democrats have remained tight-lipped on when the House will submit articles to the Senate. When she does, it could delay confirmation hearings for Biden’s nominees and his legislative agenda, which includes at its forefront a $1.9 trillion Covid relief package. 

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The Senate took up hearings for Biden’s nominees on Tuesday ahead of the inauguration, but it’s unclear whether any will be confirmed by Inauguration Day, as has occurred for each of the last four presidents.