Biden wants Congress to take action on gun reform

It's a Washington fact that pursuing 60 Senate votes can make it harder to get to 50.

It's also a Washington fact that controlling the Senate with 50 votes means there are 50 majority-makers -- and an equal number of majority-breakers.

It's a Washington theory that has Biden trying to keep both bipartisan and partisan paths alive in seeking a deal on COVID-19 relief.

In the meantime, progressives are starting to voice concerns that Biden will give too much to get Republicans on board. Senate Majority Leader Chuck Schumer has made clear he wants Republicans to negotiate with their fellow senators, as opposed to with Biden directly, while congressional leaders start the budget process on their end this week.

The kind of meeting Sen. Susan Collins, R-Maine, calls "very productive, cordial" is not going to be viewed the same way among Democrats. Then there's Sen. Joe Manchin, D-W.Va., perhaps the most conservative Senate Democrat and a vote his party needs as always, now smarting from a few perceived White House slights.

At stake are lifelines for millions of Americans, and something broader when it comes to the political system: a test of Biden's ability to govern in post-Trump Washington.

Biden's problem isn't finding dance partners. It may be that there are still too many options -- each of them still hearing different tunes.

-ABC News' Political Director Rick Klein

After nearly two hours in the Oval Office with Biden, the group of GOP senators departed -- stopping briefly for Sen. Susan Collins, R-Maine, to speak to reporters.

Collins characterize the meeting as "productive" and "cordial" but did not say that any specific progress toward a compromise had been made. 

"I wouldn't say that we came together on a package tonight," Collins said. "But what we did agree to do is 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." 

Collins said the group outlined their $600 billion package for Biden and that he explained aspects of his plan. Collins did not say how the GOP proposal was received by the president. 

She also expressed her appreciation for Biden's hosting. 

"We are very appreciative that as his first official meeting in the oval office the president chose to spend so much time with us in a frank and very useful discussion," Collins said.

The senators did not answer any questions shouted by reporters.

-ABC News' Allison Pecorin

The 10 Republican senators meeting with Biden at the White House on COVID-19 relief are expected to speak to reporters immediately following the Oval Office meeting.

The group -- led by Sen. Susan Collins, R-Maine -- includes Sens. Lisa Murkowski, R-Alaska, Bill Cassidy, R-La., Mitt Romney, R-Utah, Rob Portman, R-Ohio, Shelley Moore Capito, R-W.Va., Todd Young, R-Ind., Jerry Moran, R-Kan., Mike Rounds, R-S.D., and Thom Tillis, R-N.C.

They unveiled the details of their COVID-19 relief proposal in a letter to the president on Sunday.

Congressional Democrats have filed a joint budget resolution for the 2021 fiscal year, kicking off the reconciliation process on Biden's proposed $1.9 trillion COVID-19 relief package.

Senate Majority Leader Chuck Schumer announced the move in remarks from the Senate floor and declared that Democrats will continue to focus on "bold and robust action."

"It makes no sense to pinch pennies when so many Americans are suffering," Schumer said, echoing concerns of the White House. "The risk of doing too little is far greater than the risk of doing too much."

Schumer called the budget resolution an "additional legislative tool" to speed up COVID-19 passage, and in a joint statement with House Speaker Nancy Pelosi, said the leaders are still holding out hope for a bipartisan agreement.

"We are hopeful that Republicans will work in a bipartisan manner to support assistance for their communities, but the American people cannot afford any more delays and the Congress must act to prevent more needless suffering," Pelosi and Schumer said in a joint statement Monday afternoon.

The budget resolution will next go through a Rules Committee meeting Tuesday. Final passage in the House could occur as early as Wednesday. If the Senate amends the resolution, the House will have to pass it again before the committees could begin work on the reconciliation instructions.

The move comes ahead of Biden meeting with 10 GOP lawmakers at the White House Monday evening.

-ABC News' Mariam Khan, Trish Turner and Allison Pecorin