Some of President Trump's Republican allies are still committed to challenging the 2020 election results on the floor of the House of Representatives next month -- even as Senate Republicans have begun acknowledging Biden's status as the president-elect.

"I have a choice -- I can either fight, or I can join the surrender caucus," Rep. Mo Brooks, R-Alabama, one of the leaders of the effort to challenge the certification of the Electoral College, told ABC News.

Brooks said Monday's Electoral College vote hasn't changed his plans, but he has yet to find a GOP senator to back him. Without one, he can't force Congress to debate and vote on whether to accept a given state's slate of electors.

"This is purely performative," Michael Waldman, president of the Brennan Center, told ABC News of the long-shot challenge, comparing it to the Texas Supreme Court lawsuit that unsuccessfully sought to overturn the results in several key states.

Forcing senators on the record "purely creates political pain right now for Republicans," he said.

Republican leaders in the Senate, wary of such a vote, have also privately discouraged members from signing on.

Senate Majority Leader Mitch McConnell, soon after recognizing Biden as the president-elect, warned Republicans on a conference call that a Jan. 6 fight over electors would be a "terrible vote" and divisive for the party, sources familiar with the comments told ABC News.

-ABC News' Benjamin Siegel and Trish Turner

Biden is expected to name former Michigan Gov. Jennifer Granholm to head the Department of Energy, sources familiar with the decision confirmed to ABC News on Tuesday.

That would make Granholm, 61, the ninth woman Biden has nominated so far to serve in his cabinet. If confirmed by the Senate, the former two-term governor would be just the second woman to lead the Energy Department.

A source familiar with the transition team's thinking pointed to Granholm’s work with Biden in Michigan during the 2009 recovery that rescued the U.S. auto industry and led to investments in green energy jobs in the state -- something Biden’s ambitious infrastructure plan would also seek to invest in.

-ABC News' John Verhovek, Molly Nagle and Benjamin Siegel

Biden has announced his intention to nominate Pete Buttigieg to serve as his secretary of transportation, as earlier reported by ABC News.

If confirmed, Buttigieg, 38, would be the youngest pick yet for Biden’s cabinet and the first non-acting LGBTQ department head in history.

In a statement, Biden called Buttigieg a "patriot and a problem-solver," and said he was nominating the former mayor of South Bend, Indiana, "because this position stands at the nexus of so many of the interlocking challenges and opportunities ahead of us" -- jobs, infrastructure, equity and climate.

Buttigieg said he was honored to be asked to serve in the position.

"This is a moment of tremendous opportunity -- to create jobs, meet the climate challenge, and enhance equity for all," he tweeted following the announcement.

Biden touched down in Atlanta Tuesday afternoon to stump for Democratic Senate candidates Jon Ossoff and Rev. Raphael Warnock as the balance of power in the upper chamber -- and Biden's hopes to pass big-ticket legislation in the incoming administration -- hangs on two runoffs races in Georgia. As the first Democrat to win Georgia's presidential race since 1992, he kicked off the event by thanking supporters.

"Georgia, let me start with two simple words: Thank you," Biden said to honking horns at the drive-in rally.

"Your votes were counted and counted and counted again," Biden added with a smirk, referring to the fact that votes were counted three times in the state due to audits and recounts. "I am starting to feel like I won Georgia three times."

Biden went on to argue that Georgia "taught Donald Trump a lesson" in turning out the vote and should do the same for its Democratic contenders.

"In this election, Georgia wasn’t going to be bullied, Georgia wasn’t going to be silenced, Georgia certainly wasn’t going to stand by and let Donald Trump or the state of Texas or anyone else come in here and toss out your votes," Biden said.

"But you know, you know who did stand by? You know who did nothing while Trump, Texas and others were trying to wipe out every single one of the almost 5 million votes you had cast here in Georgia in November? Your two Republican senators, they stood by," Biden said. "You might want to remember that come Jan. 5."

"Maybe they think they represent Texas. Well, if you want to do the bidding of Texas, you should be running in Texas, not in Georgia," he added.

Calling out GOP Sens. Kelly Loeffler and David Purdue, Biden said Georgia's senators "fully embraced" nullifying five million Georgia votes -- while Ossoff and Warnock stand up for democracy, he said. Loeffler and Purdue had released a statement in support of the Texas case the Supreme Court has since refused to hear.