The U.S. Senate has voted to confirm Pete Buttigieg to lead the Department of Transportation in a 86-13 vote.

The former 2020 presidential candidate and South Bend, Indiana, mayor makes history as the first openly gay Cabinet member in U.S. history to be confirmed by the chamber.

At age 39, Buttigieg also represents another "first" as a millennial and the youngest person nominated to Biden's Cabinet.

Buttigieg has pledged to recognize how infrastructure has the power to bridge racial and economic disparities in America, as well as to keep in lockstep with Biden's agenda of fighting climate change and address systems reeling from plummeting ridership amid the coronavirus pandemic.

He will assume a department with 55,000 employees and a budget of tens of billions of dollars.

Biden and Treasury Secretary Janet Yellen will join the Democratic virtual caucus lunch Tuesday afternoon, according to Senate Majority Leader Chuck Schumer's office.

The meeting comes amid talks over next steps for COVID-19 relief and the question of whether Democrats will proceed with Biden's $1.9 trillion "American Rescue Plan" plan without bipartisan support.

-ABC News' Allison Pecorin

In floor remarks Tuesday, Senate Majority Leader Chuck Schumer said Democrats will press on with their budget resolution with a vote to proceed to consideration in the afternoon, setting up the first steps of passing COVID-19 relief through the reconciliation process.

"Time is a luxury our country does not have," Schumer said.

Schumer renewed calls for "big, bold relief" but told his Republican colleagues he welcomes their suggestions for the budget resolution.

"This process is open to bipartisanship," he continued.

Senate Minority Leader McConnell did not mention COVID-19 talks during his floor remarks but said he will vote against the confirmation of Alejandro Mayorkas to serve as Department of Homeland Security secretary, citing a 2015 inspector general report that raised questions about Mayorkas' actions in his former role at DHS.

"We are talking about shoving through green cards as political favors and intervening to overturn denials," McConnell said.

-ABC News' Allison Pecorin

House Democrats argue their case that former President Trump bears "unmistakable" responsibility for inciting the Jan. 6 riot on the Capitol, calling it a "betrayal of historic proportions" that demands judgment from the Senate in a pre-impeachment trial brief filed to the Senate Tuesday morning.

It's the first time Democrats have formally laid out their argument against Trump since transmitting the charge against him on Jan. 13 to kick off trial proceedings.

In their 80-page brief, the House impeachment managers depicted the riot as Trump's last-ditch effort to overturn the presidential election after dozens of failed lawsuits and pressure campaigns against state election officials.

"The only honorable path at that point was for President Trump to accept the results and concede his electoral defeat. Instead, he summoned a mob to Washington, exhorted them into a frenzy, and aimed them like a loaded cannon down Pennsylvania Avenue," the managers wrote in their brief submitted ahead of next week's trial of the former president.

Foreshadowing what the House managers will argue on the House floor, Democrats wrote that Trump was "reportedly 'delighted'" by the attack and "left his Vice President and Congress to fend for themselves while he lobbied allies to continue challenging election results."

The brief also argues that Trump's challenge to the results was a "direct assault on core First Amendment principles," and that holding him accountable would "vindicate First Amendment freedoms—which certainly offer no excuse or defense for President Trump's destructive conduct."

"For Congress to stand aside in the face of such conduct would be a grave abdication of its constitutional duty, and an invitation for future Presidents to act without fear of constraint during their final months in office," they wrote. "History, originalism, and textualism thus leave no doubt that the Senate has jurisdiction—and a constitutional duty—to decide this case on the merits."

-ABC News' Katherine Faulders and Benjamin Siegel