WASHINGTON (NewsNation Now) — Facing a 50-50 partisan split in the U.S. Senate, the chamber’s top Democrat and Republican discussed adopting a power-sharing deal similar to one struck two decades ago in similar circumstances, a Democratic spokesman said on Tuesday.

Democrat Chuck Schumer, set to become majority leader on Wednesday thanks to incoming Vice President Kamala Harris’ tie-breaking vote, told the chamber’s top Republican, Mitch McConnell, that he favored adopting a deal along the lines of the 2001 arrangement “without extraneous changes from either side,” a Schumer spokesman said.

Recognizing that the vice president could not be a constant presence in the chamber, the 2001 agreement split committee memberships evenly and mandated that both leaders seek to attain an equal balance of the two parties’ interests when scheduling and debating legislative and executive business.

A tax-cut package was passed then, using reconciliation with then-Vice President Dick Cheney, a Republican, serving as the deciding vote.

When one party has clear control of the Senate, it holds committee chairmanships along with a majority of committee seats and dictates the chamber’s agenda.

McConnell said last year that if the Senate did split 50-50 along party lines, he assumed the chamber would embrace a similar arrangement to that of 2001.

But in the talks with Schumer on Tuesday, McConnell also sought to keep the Senate’s legislative filibuster, according to his office. Some Democrats favor changing the rules so that legislation could pass on a simple majority vote. But McConnell wants to keep the rules requiring a super-majority of 60 votes to overcome a filibuster and advance legislation.

“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,” Doug Andres, a McConnell spokesman, said.

“Discussions on all aspects of the power-sharing agreement will continue over the next several days,” Andres said.

Republicans currently hold the majority in the Senate. But three new Democratic senators, including the winners of a pair of Georgia races and Harris’ successor, are set to be sworn in on Wednesday, creating the 50-50 split.

They have plenty of urgent business facing them in the coming days and weeks, including confirming Democratic President-elect Joe Biden’s Cabinet nominations, debating another round of COVID-19 relief and President Donald Trump’s second impeachment trial, expected after his term ends on Wednesday.

That proceeding, on a charge of inciting insurrection, could lead to a vote to ban Trump from running for office again after his supporters’ deadly Jan. 6 storming of the Capitol.

Schumer and McConnell made progress on “quickly confirming President-elect Biden’s nominees and conducting a fair impeachment trial,” the Schumer spokesman said.

The 107th Congress, in session from Jan. 3, 2001 to Nov. 22, 2002, is noted by senate.gov as “The Unforgettable 107th Congress.” On Election Day in Nov. 2000, voters knowingly elected a deceased candidate, Mel Carnahan of Missouri, to a Senate seat. That was the same election that saw former first lady Hilary Clinton elected as New York’s first female senator. Vermont Republican Sen. James Jeffords announced on May 24, 2001 he would leave his party to become an Independent and would caucus with the Democratic Party.

(Reporting by Susan Cornwell; Editing by Leslie Adler)

Reuters contributed to this report.