Biden agreed Sunday to meet with the group of 10 senators to hear their proposal, of which the group outlined the details for a $618 billion package on Monday.
The proposal includes new stimulus payments, although smaller than Biden asked for, and funding for vaccines, enhanced unemployment benefits and child care. There is no state or local coronavirus relief funding in the bill, which Democrats have long called for.
In a statement after the meeting, White House press secretary Jen Psaki said that Biden expressed hope that they could find common ground but said he would not "slow down work on this urgent crisis response" or settle for a package that "fails to meet the moment."
"While there were areas of agreement, the president also reiterated his view that Congress must respond boldly and urgently and noted many areas which the Republican senators' proposal does not address," she said. "He reiterated that while he is hopeful that the Rescue Plan can pass with bipartisan support, a reconciliation package is a path to achieve that end."
Sens. Susan Collins of Maine, who led the group, described Monday's meeting as "very productive" and "cordial" while hinting at further discussions.
"It was a very good exchange of views. I wouldn't say that we came together on a package tonight, no one expected that in a two-hour meeting. But what we did agree to do was follow up and talk further at the staff level and amongst ourselves and with the president and vice president on how we can continue to work together on this very important issue," she said.
Biden proposed a $1.9 trillion package with $1,400 stimulus payments to most Americans. The GOP package, however, calls for $1,000 payments that would go only to individual Americans earning up to $50,000 per year and married couples making up to $100,000.
Further, only individuals earning up to $40,000 and couples up to $80,000 per year would get the full payment.
The first two stimulus payments, for $1,200 and $600 last year, were given to most Americans who earned up to $75,000. Biden's proposal calls for the same terms, but Republicans in recent months have expressed concern about giving more money to people who reported higher incomes in 2019 -- which is what the criteria are based on.
Tens of millions of Americans, however, have lost their jobs since the health crisis began in early 2020.
The compromise bill also includes $160 billion for coronavirus testing and production efforts, $20 billion to reopen schools, more relief for small businesses and extended enhanced unemployment benefits of $300 a week through June.
The senators, who with Democrats could form a filibuster-proof bill, said their proposal has the best chance to earn the bipartisan support Biden is looking for.
"We recognize your calls for unity and want to work in good faith with your administration to meet the health, economic and societal challenges of the COVID crisis," said the letter from the Republican group.
In addition to Collins, the group includes Lisa Murkowski of Alaska, Bill Cassidy of Louisiana, Mitt Romney of Utah, Rob Portman of Ohio, Shelley Moore Capito of West Virginia, Todd Young of Indiana, Jerry Moran of Kansas, Mike Rounds of South Dakota and Thom Tillis of North Carolina.
Psaki said Biden remained committed to his plan and that no deal would be completed without further negotiations saying Monday's meeting was not "a forum for the president to make or accept an offer."
"The risk is not that it is too big, this package," she said. "The risk is that it is too small. That remains his view."
Senate Democratic leader Charles Schumer said he wasn't optimistic about the compromise, saying it's not even close to what Biden called for.
"We cannot do the mistake of 2009 [after the financial crisis] where they whittled down the program so that the amount of relief was so small that the recession lasted four or five years," Schumer told the New York Daily News.