US Senator Mitch McConnell (L) and new Senate Majority Leader Charles Schumer

The leaders in the Senate are switching places amid questions over whether their tepid relationship will change as Sen. Charles Schumer (D-N.Y.) becomes majority leader and Sen. Mitch McConnell (R-Ky.) becomes minority leader.

The two have as icy a relationship as there is in Washington, and few observers would predict a warming trend. Asked about the relationship, Senate Majority Whip Dick Durbin (D-Ill.) said Wednesday it has nowhere to go but up.

“It will go up,” he quipped.

Other senators are expressing hope that the Senate will become more functional under President Biden, who served 36 years in the upper chamber before becoming Barack Obama’s vice president.

“Everything is possible. You know, we have, we have administrations come and go, sometimes every four years, sometimes every eight years, and we can work with Democratic administrations and vice versa,” Sen. Lisa Murkowski (R-Alaska), a key centrist, said Wednesday.

McConnell regularly shut Schumer out of planning the Senate agenda in recent years. Most notably, he declined to negotiate a bipartisan organizing resolution for former President Trump’s first impeachment trial in the first months of 2020, a striking difference from the bipartisan resolution that passed unanimously before President Clinton’s 1999 impeachment trial.

For months last year, McConnell refused to meet with Schumer and Speaker Nancy Pelosi (D-Calif.), when Democrats were pushing for a multitrillion-dollar COVID-19 relief bill.

Broadly speaking, both men are villains for one of the  political parties. Democrats are angry at McConnell for blocking Obama’s final nominee to the Supreme Court in 2016 for months, only to quickly confirm President Trump’s nominee, Amy Coney Barrett, after Justice Ruth Bader Ginsburg’s death in the fall.

McConnell and Schumer have served in the Senate together since 1999, when Schumer came to the upper chamber from the House.

A low point in their relationship came in 2008 when Schumer, who was then the chairman of the Democratic Senatorial Campaign Committee (DSCC), used McConnell’s support for the Troubled Asset Relief Program, which critics dubbed a Wall Street bailout, against him in his 2008 reelection race.

McConnell felt Schumer, who represents New York’s financial services industry, acted in bad faith by asking for Republican support to keep banks solvent and then allowing the DSCC to blast McConnell for his vote.

The first order of business for Schumer and McConnell is to negotiate an organizing resolution to set the ratio of seats on Senate committees and divide committee resources, something likely to be difficult given the relationship between the two men.

Schumer can’t add new Democratic members to committees without such an agreement, and on some panels Republicans would continue to have more members than Democrats.

For example, there are 12 Republicans and only nine Democrats on the Senate Judiciary Committee after Kamala Harris was sworn in as vice president on Wednesday. Those numbers were set by the organizing resolution of the last Congress.

Durbin, the incoming chairman of the Judiciary panel, said Wednesday it’s not clear if he could advance Merrick Garland, Biden’s nominee for attorney general, without a new resolution. Garland is also the man Obama nominated to the Supreme Court who was blocked by McConnell and the Senate GOP.

A Republican aide said nominees can be moved through committee right now by obtaining unanimous consent from a panel’s entire membership. But that higher bar could slow the processing of Biden’s picks significantly.

Sen. Josh Hawley (R-Mo.), a potential candidate for the White House in 2024, announced Tuesday he would put a hold on Alejandro Mayorkas, Biden’s choice to head the Homeland Security Department.

McConnell this week raised the stakes of the organizing resolution by telling GOP colleagues that he would insist it include a deal to protect the legislative filibuster, which some Democrats want to eliminate to make it easier to pass Biden’s agenda.

“I believe we need to also address the threats to the legislative filibuster,” McConnell wrote in a note to GOP senators.

“Having an equally divided Senate means that we have to work together to get anything done and the spirit of true bipartisan compromise is possible only when each side realizes they must come to the table together,” he wrote.

That demand will likely delay a deal on the organizing resolution until next week, according to Senate aides.

Sen. Susan Collins (R-Maine), another key centrist, said Wednesday she supports McConnell’s effort to settle questions about keeping the legislative filibuster as part of the organizing resolution.

She noted that 61 senators, including Harris, signed a letter in April 2017 pledging support for preserving “the ability of members to engage in extended debate when bills are on the Senate floor.”

Schumer and McConnell also need to negotiate an agreement laying out the schedule and procedures for Trump’s second impeachment trial. Democrats hope to conduct the trial swiftly so that it doesn’t hold up Biden’s agenda and nominees. But limiting the amount of floor time sucked up by a trial will depend on GOP cooperation.

Republicans would need to agree unanimously to allow nominees to receive votes before the trial convenes each day at noon.

Schumer could try to pass a partisan impeachment resolution solely with 50 Democratic votes and Harris casting the tie-breaker — but he criticized McConnell harshly last year for passing an organizing resolution for Trump’s first trial without Democratic support.

He slammed McConnell’s resolution as “completely partisan” and complained “it was kept secret until the very eve of the trial” because it was “designed by President Trump for President Trump” and asked “the Senate to rush through as fast as possible

Schumer acknowledged Tuesday he will need substantial cooperation from McConnell and other GOP senators to get through a mountain of work in the next few weeks.

“Rarely — rarely — has so much piled up for the Senate as during this particular transition,” he said.

A new ingredient in the relationship is McConnell’s signals that he might vote to convict Trump in an impeachment trial. The GOP leader hasn’t ruled out a vote to convict, and if he did so it would carry heavy weight with his conference.