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The Senate is back in town Tuesday for a slate of confirmation hearings on Biden Cabinet nominees, even as there are not yet clear agreements on how the body will handle the impending Trump impeachment trial or its new 50-50 party split. 

Meanwhile, incoming Democrat senators Raphael Warnock and Jon Ossoff of Georgia, and Alex Padilla of California, won't be sworn in until Wednesday. And neither will Vice President-elect Kamala Harris, D-Calif., leaving the upper chamber in a state of limbo at least for Tuesday. 

Also looming is the fact that House Speaker Nancy Pelosi, D-Calif., hasn't yet sent over the article of impeachment passed last week accusing President Trump of inciting an insurrection.

Outgoing Senate Majority Leader Mitch McConnell, R-Ky., put out guidance last week saying that the earliest the Senate could start an impeachment trial was 1 p.m. on Jan. 20, an hour after President-elect Joe Biden is sworn in. But that would only be possible if Pelosi sends the articles Tuesday or earlier. A delayed impeachment trial is looking more likely, as Senate Minority Leader Chuck Schumer, D-N.Y., emphasizes the Senate's need to keep many plates spinning all at once. 

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"Well, we have the trial of the president. That's mandated by law," Schumer said in an interview on CBS' "60 Minutes" Sunday. "Second, there's a very, very real need for President Biden to have in place key people in his Cabinet, the people in charge of national security, the people in charge of domestic security, the people in charge of making sure everyone gets vaccinated as quickly as possible."

He added: "And third, this country is in the greatest economic crisis since the Depression, the greatest health care crisis since the Spanish pandemic flu 100 years ago, and we must pass more relief for the American people. We must do all three and we have to do them all quickly. One cannot stand in the way of the other."

The shorthanded Senate is taking a bite out of at least one of its outstanding tasks on Tuesday, holding five hearings for some of Biden's nominees. 

At 10 a.m. the Senate Committee on Finance began its interview with Janet Yellen, the nominee for secretary of the treasury. The former chair of the Federal Reserve is relatively uncontroversial and is expected to have more than enough GOP support for a smooth confirmation, though the timing, as with all of the Biden nominations, is still unclear. 

Yellen in her hearing advocated for the U.S. to act boldly on economic stimulus with interest rates at historically low levels. 

At the same time, the Senate Intelligence Committee started examining Biden's pick for director of national intelligence, Avril Haines, and the Homeland Security and Governmental Affairs Committee started a hearing with expected Homeland Security secretary nominee Alejandro Mayorkas. 

Federal Reserve Chairman Janet Yellen waits for a hearing of the Joint Economic Committee on Capitol Hill, Nov. 29, 2017, in Washington, D.C.

Federal Reserve Chairman Janet Yellen waits for a hearing of the Joint Economic Committee on Capitol Hill, Nov. 29, 2017, in Washington, D.C. (BRENDAN SMIALOWSKI/AFP via Getty Images)

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Mayorkas' hearing, with controversy on border security and the siege of the Capitol swirling, is expected to be testy at times. It started out with stark partisan disagreement on Mayorkas' qualification for his position. 

Sen. Diane Feinstein, D-Calif., started the Mayorkas hearing detailing his career and her long professional relationship with him, which she said began in the 1990s when she recommended that former President Bill Clinton choose the Cuban immigrant as a U.S. Attorney. 

"I believe [Mayorkas] is uniquely qualified to face the challenges before DHS," she said. "The United States faces substantial security concerns and threats. And I just would like this committee to know that this senator has full confidence that [Mayorkis] will provide positive leadership and strongly urge this committee to support his nomination."

But Sen. Rob Portman, R-Ohio, who for at least Wednesday is the chairman of the Homeland Security and Governmental Affairs Committee, outlined a previous Senate confirmation for Mayorkas at which Republicans uniformly opposed him because he was under investigation by the DHS inspector general. 

Alejandro Mayorkas, nominated by President-elect Biden as Homeland Security Secretary.

Alejandro Mayorkas, nominated by President-elect Biden as Homeland Security Secretary.

"Today, we have the findings of that inspector general report, and they are concerning," Portman said. The IG, the senator continued, found that Mayorkas "'communicated with stakeholders on substantive issues outside of the normal adjudicatory process and intervened with career USCIS staff in ways that benefited the stakeholders.'"

"Equally concerning is the testimony from DHS whistleblowers regarding MR. Mayorkas' management style. One witness stated that encounters with Mr. Mayorkas were 'uncomfortable, aggressive, unusual and unsettling."

Sen. John Tester, D-Mont., meanwhile lauded Mayorkas as "made for public service" and urged the Senate to quickly confirm him after the attack on the Capitol, saying "we have no time to waste."

Sen. Mitt Romney, R-Utah, meanwhile, grilled Mayorkas on what he would do with the migrant caravan coming to the U.S. from Central America, accusing him of providing an "uncertain" answer about whether his DHS will allow the caravan to burst through the border or if they will be stopped and processed one-by-one. 

"I apologize if I was uncertain," Mayorkas said. "If people qualify under the law to remain in the united states, then we will apply the law accordingly. If they do not qualify to remain in the United States, then they won't."

At the hearing for Haines, the nominee said that if confirmed she will release a public assessment of the threat of QAnon as well as an unclassified report on who was responsible for the death of Jamal Khashoggi.

Haines also told senators that she supports an "aggressive stance" against China, one that would be more "assertive" than what was taken by the Obama-Biden administration in which she previously served.

Later in the day, the Senate Foreign Relations Committee will examine Biden's secretary of state pick Anthony Blinken and the Armed Services Committee will interview Lloyd J. Austin, Biden's choice for defense secretary. 

Austin is a well-respected general who was the commander of United States Central Command under former President Barack Obama. But he will be assuming a civilian position as defense secretary. The holder of that office, under the law, must be out of uniform for seven years. Lloyd has been retired for just under five years.

A waiver to this requirement from both chambers was granted for former Trump Defense Secretary Jim Mattis, who was Lloyd's predecessor at the U.S. Central Command. But many have said the Mattis situation was unique. There was serious distrust of President Trump on Capitol Hill at the time and lawmakers were happy to install a respected general into his Cabinet. 

Austin, however, is expected to have the necessary support to be confirmed, perhaps second only to Yellen. The other nominees are expected to face more suspicion from Republicans. 

Sen. Chris Murphy, D-Conn., on Monday said he would support the Austin confirmation after in 2017 voting against a waiver for Mattis, using the opposite logic of many who backed Mattis but are now suspicious of granting a waiver for Austin.

"The internal security threat the U.S. faces right now is serious. We need a Secretary of Defense on the job immediately. I will vote to confirm Lloyd Austin and grant him a waiver, and I urge other Senators to do the same," Murphy tweeted Monday. 

"A general at DoD was especially worrying under Trump. Trump had zero foreign policy experience, a penchant to glorify violence, a total neophyte Secretary of State, and an unstable, war mongering former general as NSA," Murphy added. "All of this is different under Biden. Biden has loads of experience and a built in healthy skepticism of military action. The balance of power in his national security team lies with Blinken, Sullivan, Burns, Power, Kerry, Thomas-Greenfield, all diplomats."

How quickly these confirmations happen, however, will be up to Schumer and McConnell. They've yet to announce an agreement on how the Senate will split its time between impeachment and other business, if it will at all. During the previous Trump impeachment trial, the Senate met every day but Sundays for the trial (as it is required to) and handled no other business. 

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Biden previously suggested that the Senate could "go a half-day on dealing with impeachment, a half-day on getting my people nominated and confirmed in the Senate, as well as moving on the [Biden coronavirus] package." 

Schumer and McConnell will meet in person on Tuesday, and that is part of what they will discuss. If Pelosi continues to hold on to the impeachment article, however, no such agreement will be necessary. Although the Senate must move immediately on an impeachment trial once the House sends an article of impeachment, it can't do anything until the article is transmitted. 

President-elect Joe Biden speaks during an event at The Queen theater, Thursday, Jan. 14, 2021, in Wilmington. Hearings on Biden's Cabinet nominees are set to begin Tuesday. 

President-elect Joe Biden speaks during an event at The Queen theater, Thursday, Jan. 14, 2021, in Wilmington. Hearings on Biden's Cabinet nominees are set to begin Tuesday.  (AP Photo/Matt Slocum)

Pelosi's office has not responded to multiple requests for comment on when she may send the impeachment article to the Senate. 

Also on the agenda for Schumer and McConnell is a power-sharing agreement for once Padilla, Warnock, Ossoff and Harris are sworn in. Punchbowl News reported Friday that the 2001 accord between Sens. Trent Lott, the Republican leader at the time, and Tom Daschle, then the Democrat leader, is the template for these negotiations. 

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Under that agreement, there was technically a minority and majority leader — in this case, Schumer would be the majority leader because Harris will be the vice president. 

And each party was given equal representation on committees, to reflect the evenly split body. In most cases, the majority party is given more seats on Senate committees. Under the 2001 arrangement, there were mechanisms for legislation to make it out of committee if a vote was tied. 

Also in 2001, Daschle, the minority leader, could bring some bills to the Senate floor. It's unclear if that minority right might be included in a power-sharing agreement between Schumer and McConnell. 

The offices of Schumer and McConnell did not immediately respond to requests for comment on asking about the details of a potential agreement between the two leaders. 

Fox News' Chad Pergram, Adam Shaw, Lawrence Edward, Mike Emanuel and The Associated Press contributed to this report.