Senate Majority Leader Charles E. Schumer (D-N.Y.) said Tuesday that the Senate could vote as soon as next week on a budget bill setting the stage for party-line passage of President Biden’s $1.9 trillion pandemic relief plan.

“The work must move forward, preferably with our Republican colleagues but without them if we must,” Schumer said. “Time is of the essence to address this crisis.”

Schumer spoke at a news conference a day after Minority Leader Mitch McConnell (R-Ky.) signaled he would move forward with a power-sharing agreement governing operations of the 50-50 Senate.

McConnell had sought assurances from Schumer that Democrats would not eliminate the filibuster, the 60-vote supermajority requirement to move most legislation. Schumer refused, but after two centrist Senate Democrats committed publicly to upholding the filibuster, McConnell relented.

Senate Minority Leader Mitch McConnell (R-Ky.) defended the filibuster, a key Senate rule McConnell wants to keep in a power-sharing deal with Democrats. (The Washington Post)

McConnell’s capitulation ended a days-long standoff that had held up Senate operations and threatened to stall Biden’s agenda before it could even get off the ground.

“I’m glad we’re finally able to get the Senate up and running,” Schumer said. “My only regret is that it took so long.”

The first priority for Biden and congressional Democrats is action on a new covid-19 relief package at a precarious moment for the pandemic and the economy.

Publicly, the Biden administration is courting Republican support, and Schumer held out hope of GOP backing. But a number of leading Republicans including McConnell have panned Biden’s plan as too costly, and behind the scenes Democrats are making plans to move forward without them.

Democratic leaders in both chambers are tentatively planning to introduce a budget resolution on Monday that could come to a vote later in the week, according to several people with knowledge of the plans who spoke on condition of anonymity to discuss them.

The resolution would instruct committees to write legislation codifying Biden’s $1.9 trillion pandemic relief plan. Under special rules governing the budget resolution, the resolution could pass the Senate with a simple majority vote, and the subsequent covid-19 relief bill could also pass with a simple majority -- even without eliminating the filibuster.

Getting all Senate Democrats unified behind the plan could prove a challenge, especially since some have expressed discomfort with some aspects of it. But Schumer insisted Tuesday his caucus was unified on the need to do big things, and he also said that proceeding under “budget reconciliation” did not preclude Republican votes.

Sen. Bernie Sanders (I-Vt.), chairman of the Senate Budget Committee, told reporters: “We’ve got to move as quickly as we can. . .Elections have consequences.”

Biden’s plan provides for a new round of $1,400 stimulus checks, an extension of emergency unemployment benefits, an increased child tax credit, more than $130 billion for schools, $160 billion for a national vaccination strategy, and an increase in the federal minimum wage to $15 an hour. There’s money for rental assistance and extending an eviction moratorium.

Enhanced unemployment benefits are set to expire in mid-March if Congress does not act first, as are moratoriums on evictions and foreclosures. Administration officials and congressional Democrats point to that deadline as underscoring the need for fast action.

“It’s critical ... that we don’t get anywhere near the March cliff,” White House press secretary Jen Psaki said Tuesday. “People need security, and what we’re trying to do now is provide that.”

The administration has been in discussions with a 16-member bipartisan group that has raised issues including whether stimulus checks could be more targeted, something Biden indicated Monday he is open to.

Sen. Mark R. Warner (D-Va.), one member of the bipartisan group, indicated openness Tuesday to moving via reconciliation, saying: “I think you’ve got to keep all of your options open.”

Democrats are attempting to move quickly to take the first steps advancing the coronavirus relief legislation, partly because the Senate is set to convene the week of Feb. 8 to start former president Donald Trump’s impeachment trial., which will take an unknown period of time.

The dispute over the filibuster lingered Tuesday as McConnell warned Democrats that Republicans would counter any attempt to eliminate it with “immediate chaos” that would grind the chamber — and the Democratic governing agenda — to a halt.

Republicans, he said, would exercise their rights to object to routine business and demand frequent quorum calls — procedural feints that would grind business to a standstill and require senators and Vice President Harris to be on constant standby for roll-call votes.

“None of us on either side want to live in a scorched-earth Senate,” McConnell said. “This gambit would not speed the Democrats’ ambitions. It would delay them terribly.”

McConnell said Tuesday a further escalation would mean Senate business would move at “a snail’s pace” and “drain comity and consent from this body to a degree that would be unparalleled in living memory.”

McConnell’s threats are not likely to defuse the tension inside the Democratic ranks over whether to “go nuclear” in the future, as Senate rules changes have come to be called by members of both parties. But the agreement to move forward with the power-sharing deal likely means the issue is on the back burner for the time being.

That deal means that committees can be reconstituted with new members and Democratic chairs after a five-day standoff where the GOP kept control of most committees despite Democrats having a majority on the floor, thanks to Vice President Harris’s tie-breaking vote.

Jeff Stein contributed to this report.