Republicans are proposing the full $1,000 checks for individuals earning above $50,000 and couples earning about $100,000.
"With this budget resolution, the Democratic Congress is paving the way for the landmark Biden-Harris coronavirus package that will crush the virus and deliver real relief to families and communities in need", the Democratic leaders said.
Biden responded by inviting the Republican lawmakers to the White House this week for talks, spokesperson Jen Psaki said, even as he continues to seek a comprehensive, large-scale measure. "The only thing we can not accept is a package that is too small or too narrow to pull our country out of this emergency", Schumer said.
The senators said in a joint statement that they were "pleased to accept" the President's invitation.
Republicans contended that "billions of dollars remain unspent" from the $900 billion December CARES Act package, while more money from the March version "has yet to be exhausted".
But Brian Deese, director of the National Economic Council, told NBC's "Meet the Press" program that the Democratic president was not willing to compromise on the need for a wide-ranging bill to address the public health crisis and economic fallout. Bill Cassidy, R-La., who told Fox News that Biden made no effort to work with his bipartisan group.
Ten Republican votes, combined with the backing of 50 Democrats and independents, would be enough to move bipartisan legislation quickly through the Senate.
Schumer spoke ahead of the Oval Office meeting between Biden and 10 Republican senators, who have proposed a scaled-down US$618 billion relief package.
"Covid relief can't wait any longer", said Rep. Pramila Jayapal (D-Wash.), chair of the CPC. House Speaker Nancy Pelosi said Congress would complete a preliminary step before the end of the week.
Some Republicans have questioned the overall price tag, while others urged more targeted measures, particularly over the direct payments to individuals.
But Biden's COVID-19 agenda could also be slowed by partisan politics as the Senate moves toward a February 9 impeachment trial of former Republican President Donald Trump, who faces a charge that he incited insurrection with a fiery speech to supporters just before hundreds of them stormed the Capitol on January 6.
Coronavirus stimulus checks: who would get checks?
The United States leads the world in Covid-19 cases and deaths by a large margin.
"It's important to remember that the size of the package was designed with the size of the crisis-dual crises, as we've said", Psaki said. Jacky Rosen and Catherine Cortez Masto of Nevada, released a letter they sent to the two Senate leaders, detailing the layered challenges for states with overburdened unemployment systems, schools struggling with remote learning, and small businesses unable to access loans.
"The QAnonGOP jammed through tax cuts and goodies for their corporate pals", Tlaib tweeted, referring to Republicans' use of the budget reconciliation process in 2017 to pass their $1.5 trillion tax bill with a simple-majority vote.