Speaker Nancy Pelosi and Senate Majority Leader Charles E. Schumer gave the clearest signs yet they are ready to plow ahead next week with the budget reconciliation process for a filibuster-proof coronavirus relief package.

In separate remarks, the Democratic leaders said they would bring the fiscal 2021 budget resolution to the floor in both chambers — if only, they stressed, as a backstop in case Republicans won’t cooperate on a bipartisan measure.

“We’re going to bring a budget resolution to the floor next week and then we’ll send it over to the Senate. Then if they change it, then we’ll take it back and address it,” Pelosi told reporters Thursday. “But by the end of the week, we will be finished with the budget resolution, which will be about reconciliation, if needed. And I hope we don’t need it. But if we need it, we will have it.”

According to sources familiar with the planning, the House budget blueprint will be introduced Monday, go before the Rules Committee on Tuesday and hit the floor on Wednesday.

It will contain instructions for various authorizing committees to produce a reconciliation package that would add no more than $1.9 trillion to deficits over 10 years. That’s in line with President Joe Biden’s proposed COVID-19 aid bill, but the details will be up to the committees of jurisdiction who could add to or subtract from provisions in the White House proposal.

In opening remarks on the Senate floor, Schumer said “as early as next week” his chamber would “begin the process” of putting together a relief bill, which an aide clarified meant taking up a budget resolution.

“Our preference is to make this important work bipartisan, to include input, ideas and revisions from our Republican colleagues, or bipartisan efforts to do the same,” Schumer said. “But if our Republican colleagues decide to oppose this urgent and necessary legislation we will have to move forward without them.”

A bipartisan 16-member Senate group has been working with the White House to find common ground, but there are only eight GOP members of the group and Democrats have only 50 votes on their side — not enough to get over the usual 60-vote hurdle. And it’s not clear any of the eight Republicans in the talks will support Biden’s $1.9 trillion plan.

Senate Majority Whip Richard J. Durbin said a final decision hadn’t been made to go forward with a budget next week but noted “we’re considering that as a very real possibility.” He said the process could involve a lengthy “vote-a-rama” of amendments as is typical, which he called “the worst.”

“Seriously, every time there has been a vote-a-rama, all the pent-up energy of would-be legislators is manifest on the floor. And we usually go through 40, 50, 60 amendments of dubious quality and members have their day. And under the rules it’s their right to do it,” Durbin said.

Durbin said he expects this amendment voting process to be particularly challenging given the frustration throughout Capitol Hill.

Sen. Jerry Moran, R-Kan., a member of the bipartisan group, cited those dynamics and the fact that Democrats can’t afford any defections given the 50-50 balance of power as reason they should be working with Republicans instead of pursuing reconciliation.

“They’d have to have every member and just the process of a budget is so time consuming, so many votes — lots of politics seem to arise in those circumstances,” he said. “I would encourage the administration, but certainly Senator Schumer and the Democrat majority, to work with Republicans.”

One Democratic senator in the bipartisan group, West Virginia’s Joe Manchin III, repeatedly declined to say Thursday whether he would vote for the budget resolution needed to set up reconciliation. “We’re gonna try to make Joe Biden successful,” Manchin said in response to several questions about how he would vote.

Democrats also have to contend with the possible absence of Sen. Mark Warner, D-Va., who is self-isolating after a possible COVID-19 exposure, could change that timeline given the 50-50 balance of power. “We certainly need him,” Durbin said. If Warner gets back early in the week, Democrats could get the simple majority they need to proceed to the budget resolution.

Both chambers need to adopt the same numbered concurrent budget resolution. People close to the process said the House and Senate budget blueprints are expected to be more or less identical to prevent them from having to reconcile two separate versions.

Democrats want to begin the process of writing the reconciliation bill the week of Feb. 8, to give themselves enough time for both chambers to send it to Biden’s desk before enhanced unemployment benefits run out March 14. The earliest the House could take up the reconciliation package under its current schedule is the week of Feb. 22.

Paul M. Krawzak contributed to this report.