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

Following a briefing with his COVID-19 advisory team on Tuesday, Biden is expected to continue his criticism of the Trump administration in afternoon remarks on the coronavirus pandemic from Wilmington, Delaware, and home in on what his team has characterized as the lagging pace of vaccine distribution.

According to a transition official, Biden will provide an update on the current state of the pandemic and give a dire prediction that, tragically, infection and death rates will rise in the coming weeks. Biden is also expected to address the current administration falling short on its pace for vaccinations, the official said, as well as his plan to get 100 million vaccinations in 100 days.

Biden on Monday slammed the Trump administration for, he said, leaving security agencies "hollowed out" and for creating "roadblocks" for his transition team seeking access to key national security information -- a comment that acting Defense Secretary Christopher Miller has pushed back on, saying the Biden team has already been given more interviews and documents than they initially requested.

Vice President-elect Kamala Harris and her husband, Doug Emhoff, on Tuesday morning are slated to receive their first doses of the COVID-19 vaccine in Washington, D.C., where Harris may also comment on the incoming administration's vaccine distribution plans.

Trump, meanwhile, continued to contest the election on Twitter Tuesday morning -- with three weeks until Biden's inauguration -- criticizing Republican leadership as "pathetic," saying they "only want the path of least resistance" and "only know how to lose." He also attacked Republican lawmakers over their handling of the defensing funding bill as the Senate is expected to override Trump's presidential veto for the first time in his presidency by the end of the week.

After Trump changed course on Sunday and signed the coronavirus relief and government funding bill to avert a shutdown -- though not in time to prevent unemployment benefits to millions of Americans from lapsing -- the House of Representatives on Monday approved Trump's call to increase the coronavirus relief payments from $600 to $2,000.

But its fate in the Senate is uncertain. Senate Majority Leader McConnell has declined to reveal how he will proceed or even whether he’ll bring the proposal up for a vote. Democrats are seizing the opportunity to force Republicans into a difficult position -- either backing or defying Trump.

-ABC News' Molly Nagle and Ben Gittleson