When President George W. Bush was elected, Republican Sen. Trent Lott of Mississippi became Senate majority leader with the Texan's January 20, 2001 inauguration.

At the time, the Senate was split 50-50 between the two parties, with the Republicans retaining chairmanships in committees -- but Lott worked with Senate Minority Leader Tom Daschle of South Dakota in a landmark power-sharing agreement that provided both parties with equal committee representation among other features.

At the time, Lott said he did not want a "prescription for gridlock" and sought to work across the aisle to maintain the productivity of the Senate.

The two former senators joined "Bill Hemmer Reports" on Tuesday to discuss their experience, and how it relates to the prospect of another 50-50 Senate split, pending the outcome of two Senate runoff elections in Georgia on Jan. 5.

"[Tom Daschle and I] have been through a lot of things together and worked through tough times," Lott said. "On the election there is a process, legal actions and investigation. At some point that will end. It looks like Joe Biden will be the president-elect. Then the challenge will be how do you deal with Congress?"

If Republicans prevail in Georgia, the issue becomes moot and Senate Majority Leader Mitch McConnell, R-Ky., fully retains his current leadership role, he said.

"If we lose it will be 50-50. That’s a challenge. Tom Daschle and I found a way to work through it. We had a good chemistry. I trusted him and respected him," he continued. "He was a leader of the other party. We had to make it work."

He described how the two met to negotiate the 2000 power-share agreement and pointed to the accomplishments the Senate was able to pass, including the No Child Left Behind Act.

"A lot of credit goes to Tom Daschle and the fact we worked together to make the best of a tough situation," the former Mississippi lawmaker said.

Daschle later reflected as well on his own experiences in 2000, a position McConnell may find himself in with Sen. Charles Schumer of New York in a majority leader role due to Vice President-elect Kamala Harris' position as president of the Senate, should Democrats gain the two Georgia seats.

"I have to give Trent a lot of credit as well. He was the majority leader going into this. We had to work through a lot of challenges. I take your point about being divided. We were very divided back then. We had an impeachment back then and a very, very close election [resolved] by the Supreme Court," the South Dakotan said.

"In spite of that division, what you have to do is recognize it and know there are many challenges and then build the chemistry among those who are expected to lead both in Congress and in the White House."

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Daschle said leaders of both parties as well as the incoming Biden administration need to commit to working together in order for a divided Senate to be productive.

In 2000, Daschle began the new Congress as majority leader due to the fact Al Gore remained as vice president until Jan. 20, 2001.

Lott's majority leader title rebounded back to Daschle later that year when then-Sen. Jim Jeffords, R-Vt., left the GOP to become an Independent and began caucusing with the Democrats.