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

Russ Vought, the current director of the Office of Management and Budget, struck back at President-elect Joe Biden's transition team one day after it leveled allegations that Trump's OMB was hindering the incoming team.

In a lengthy letter detailing what he says are a number of falsehoods, Vought wrote that Biden's team made false accusations about the OMB and said they fully participated in appropriate transition efforts -- including over 45 meetings.

"As the record shows, OMB has fully participated in appropriate transition efforts," Vought wrote. "What we have not done and will not do is use current OMB staff to write the [Biden transition team]'s legislative policy proposals to dismantle this Administration's work. OMB staff are working on this Administration's policies and will do so until this Administration's final day in office."

"Redirecting staff and resources to draft your team's budget proposals is not an OMB transition responsibility," he added.

In a weekly press conference Wednesday, Biden transition spokesman Yohannes Abraham criticized the Trump administration for failing to cooperate with their agency review teams, particularly with political leaders at OMB.

"In normal transitions -- this was the case in 2008, it was the case in 2016 -- OMB career staff provide critical analytical support to incoming administrations as they look towards the execution of their priorities and the production of their budget," Abraham said. "That analytical support has not been forthcoming from OMB. And there have been no signs that it is -- it will be forthcoming in the days to come."

-ABC News' Elizabeth Thomas and Molly Nagle