"We urge him to sign this bill into law to give immediate relief to hardworking families," Pelosi, D-Calif., tweeted.
The enrollment comes after House Republicans rejected the president's demand for $2,000 checks for most Americans. The rare Christmas Eve session of the House lasted just minutes, with help for millions of Americans awaiting Trump's signature on a smaller COVID relief and government funding bill.
Trump's refusal of the $900 billion package, which is linked to a $1.4 trillion government funding bill, could spark a federal shutdown at midnight Monday. His push to increase direct payments for most Americans from $600 to $2,000 for individuals and $4,000 for couples has gotten support from Democrats but splits the GOP.
The Senate cleared the relief package on Monday by a 92-6 vote after the House approved it 359-53. Those vote totals would be enough to override a veto should Trump decide to take that step.
Senate Majority Leader Mitch McConnell, R-Ky., and House Minority Leader Kevin McCarthy, R-Calif., helped negotiate the year-end deal, a prized bipartisan compromise that won sweeping approval in the House and Senate after the White House assured GOP leaders that Trump supported it.
Treasury Secretary Steven Mnuchin boasted that the $600 checks all sides had agreed to for Americans would in the mail in a week.
Democrats will recall House lawmakers to Washington for a vote Monday on Trump's proposal, with a roll call that would put all members on record as supporting or rejecting the $2,000 checks. They are also considering a Monday vote on a stop-gap measure to at least avert a federal shutdown, keeping the government running until President-elect Joe Biden is inaugurated next month.
Even if the House is able to approve Trump's $2,000 checks on Monday, that measure would likely die in the GOP-controlled Senate, which is due back in session on Tuesday.
The Associated Press contributed to this report.