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

Biden took aim at Trump in remarks following a briefing on national security and foreign policy, slamming the current administration for failing to fully cooperate with his agency review teams during the transition -- which Biden argued could leave the country vulnerable.

While commending his own agency review teams for their hard work amid a transition that was already made more challenging by COVID-19, Biden pointedly called out Department of Defense and White House Office of Budget and Management political appointees for, he said, not cooperating for a smooth transition.

"And the truth is many of the agencies that are critical to our security have incurred enormous damage. Many of them have been hollowed out in personnel, capacity and in morale," Biden added.

Later in his remarks, Biden stressed the need for cooperation during the transition, noting that it is a matter of national security to ensure there are no gaps that adversaries can seek to exploit when he takes office.

"We need full visibility into the budget planning under way at the Defense Department and other agencies in order to avoid any window of confusion or catch-up that our adversaries may try to exploit," Biden said. "Right now, we just aren't getting all the information that we need from the outgoing administration in key national security areas. It's nothing short, in my view, of irresponsibility."

Biden said other "Day One" challenges discussed in the briefing will draw on the skill sets of the Department of Homeland Security and the Federal Emergency Management Agency as they aim to "clean up the humanitarian disaster that the Trump administration has systematically created on our Southern border."

"We will institute humane and orderly responses. That means rebuilding the capacity we need to safely and quickly process asylum seekers, without creating near-term crises in the midst of this deadly pandemic," Biden said.

As he exited the stage at the Queen Theater in Wilmington, Delaware, Biden was asked if he supports the measure for $2,000 direct payments to Americans for COVID-19 relief, which the House will soon vote on. He responded with one word: "Yes."

-ABC News' Molly Nagle, Sarah Kolinovsky and Beatrice Peterson