In a statement, Senate Democratic Leader Chuck Schumer, D-N.Y., said he would try to get the House-approved bill to provide $2,000 emergency checks passed in the Senate on Tuesday.

"Following the strong bipartisan vote in the House, tomorrow I will move to pass the legislation in the Senate to quickly deliver Americans with $2,000 emergency checks. Every Senate Democrat is for this much-needed increase in emergency financial relief, which can be approved tomorrow if no Republican blocks it – there is no good reason for Senate Republicans to stand in the way," he said in the statement. "There's strong support for these $2,000 emergency checks from every corner of the country -- Leader McConnell ought to make sure Senate Republicans do not stand in the way of helping to meet the needs of American workers and families who are crying out for help."

Acting Secretary of Defense Christopher Miller pushed back on Biden's claim earlier Monday about transition interference by the Department of Defense in a statement.

"The Department of Defense has conducted 164 interviews with over 400 officials, and provided over 5,000 pages of documents – far more than initially requested by Biden's transition team. DoD's efforts already surpass those of recent administrations with over three weeks to go and we continue to schedule additional meetings for the remainder of the transition and answer any and all requests for information in our purview. Our DoD political and career officials have been working with the utmost professionalism to support transition activities in a compressed time schedule and they will continue to do so in a transparent and collegial manner that upholds the finest traditions of the Department. The American people expect nothing less and that is what I remain committed to."

The House narrowly passed a bill that would increase the amount of money Americans receive in a second round of pandemic relief stimulus payments to $2,000, up from $600.

The final vote tally was 275-134, receiving the two-thirds majority it required under the expedited vote. There were 44 Republicans who voted with Democrats.

Even though Trump supports the measure, a number of Republicans voted against the bill. Its fate remains uncertain in the Senate.

The House vote comes one day after Trump signed the $2.3 trillion spending and COVID-19 relief bill, which included $600 stimulus checks for Americans who make $75,000 or less. Trump initially threatened to hold up the bill last week and said it was a "disgrace." He spent the next several days calling on Congress to pass a bill that included $2,000 stimulus checks instead.

Democrats took up Trump's offer last week and attempted to pass a bill that would send Americans $2,000 checks via unanimous consent but that attempt failed over Republican objections. House Speaker Nancy Pelosi vowed to bring the bill to the floor for a full recorded vote on Monday.

Even though the bill has now cleared the House, at this point it's unclear if the Republican-led Senate will bring the bill to the floor for a vote. Senate Majority Leader Mitch McConnell made no promises in his statement Sunday when he commended the president for finally signing the COVID-19 relief bill into law.

Pelosi called on Trump to put more pressure on his party to back the payments.

"Every Republican vote against this bill is a vote to deny the financial hardship that families face and to deny the American people the relief they need," she said in a statement released Sunday.

Senate Minority Leader Chuck Schumer said Sunday that he would try to pass the legislation in the Senate.

"No Democrats will object. Will Senate Republicans?" he tweeted.

-ABC News' Mariam Khan

In another far-fetched effort to overturn the election results, Texas Rep. Louie Gohmert and Republican electors in Arizona filed a suit in the U.S. District Court in the Eastern District of Texas on Sunday, attempting to push Vice President Mike Pence into using alternate electors from the battlegrounds in the congressional certification on Jan. 6.

The lawsuit argues that Pence has the power as the president of the Senate to choose the alternate electors when Congress formalizes the Electoral College vote.

Gohmert argues that alternate electors in Arizona, Georgia, Michigan, Pennsylvania and Wisconsin should be tapped "as a result of the extraordinary events and substantial evidence of election fraud and other illegal conduct before, during and after the 2020 general election in these states."

According to filings, there is no response in the docket from Pence thus far, but U.S. Attorney Stephen Cox and acting Attorney General Jeffrey Rosen have been served with documents. Judge Jeremy Kernodle is presiding.

-ABC News' Meg Cunningham and Political Director Rick Klein

In her first meeting as interior secretary-designee, Deb Haaland hosted a virtual roundtable with tribal leaders on Monday morning, according to the Biden transition team.

Joined by incoming senior adviser to the president and director of the White House Office of Public Engagement Cedric Richmond and incoming director of the White House Office of Intergovernmental Affairs Julie Rodriguez, Haaland “reiterated President-elect Joe Biden’s promise to Tribal Nations and indigenous communities to fully honor America’s sacred trust and treaty obligations to Tribal Nations,” the transition said in a readout of the meeting.

“They also discussed how the incoming Biden-Harris Administration will work in coordination with tribal communities who bear disproportionate harm from long-running environmental injustices and are being adversely affected by the impacts of climate change on their homelands,” the readout continued.

Haaland addressed Biden’s ambitious climate policy during the meeting, discussing the incoming administrations plans to address the inequities of global warming and efforts to address climate change, treating it as an economic opportunity. She also pledged to ensure that the Interior Department engages in "early, frequent, and meaningful consultation" with tribal leaders on decisions that affect indigenous communities, according to the readout.

If the Senate confirms her as secretary of the interior, Haaland would be the first Native American to serve in a presidential Cabinet and would be the first Native person to oversee an agency that's played a major role historically in the forced relocation and oppression of Indigenous people.

-ABC News' Molly Nagle