“I am not going to start by breaking a promise to the American people,” he added about direct payments.

Biden’s message to the caucus comes as Democrats race to deliver the president’s first legislative priority, a sprawling coronavirus relief plan that so far lacks support from Republicans in Congress. One key sticking point so far has been over the stimulus checks, with some centrist Democrats — and many GOP lawmakers — calling for stricter income limits on the direct payments.

“We can better target the number, I’m OK with that,” Biden told House Democrats, according to multiple sources on the call.

But Biden also made clear that he would not shrink the overall size of his package to meet GOP demands. After a lengthy meeting Monday with GOP senators who pitched a $618 billion plan, Biden told Democrats that offer “was not even in the cards.”

Biden also met with a group of Senate Democrats for roughly 90 minutes on Wednesday, as the Senate prepares to adopt its own budget this week.

Senate Majority Leader Chuck Schumer described the meeting at the White House as “substantive” and said Democrats agreed to a “big and bold” approach.

“We want to do it bipartisan, but we must be strong,” Schumer told reporters after the meeting. “We cannot dawdle, we cannot delay, we cannot dilute, because the troubles that this nation has and the opportunities that we can bring them are so large.”

“I think we’re leaving open the possibility of Republicans working with us but I think the bottom line is we have to deliver,” added Sen. Brian Schatz (D-Hawaii), who was also present.

The House will vote later Wednesday on a budget measure that marks the critical first step toward muscling Biden’s package through Congress without GOP votes. Democrats are confident they have the votes to adopt the budget, though there is some lingering anxiety among several moderate Blue Dog Democrats that the party should move other smaller relief bills as they wade into the thornier process known as reconciliation.

Speaking on the House Democratic call, Biden acknowledged that some lawmakers, including Republicans, get “hung up” on the price tag when the nation is already facing a ballooning federal deficit and skyrocketing debt. Congress has passed nearly $4 trillion in assistance since the beginning of the pandemic.

The economy is expected to bounce back over the next several months, even without more stimulus aid from Congress, the Congressional Budget Office said earlier this week. But employment levels are unlikely to fully recover until 2024.

“We have to get this done. I’m not married to a particular, absolute number,” Biden said of the overall cost, noting that Democrats “can make compromises on several of the programs.”

Those estimates are “important,” Biden said of the Congressional Budget Office scores that tally the total price tag, “but what I’m thinking about is, who are we helping?”

At one point on the call before Biden joined, Rep. Sheila Jackson Lee interrupted the broader policy discussion to ask about redistricting. Speaker Nancy Pelosi herself interjected and steered the conversation back to the coronavirus relief bill, urging the caucus to “pass the budget bill with complete unity,” according to multiple people on the call.

Democrats are largely united behind Biden’s relief proposal, which would deliver badly needed money for vaccine distribution, small businesses and schools — in addition to raising the minimum wage to $15-an-hour and creating a national paid family leave program.

But top House and Senate Democrats still face some headwinds in the party about their party-line approach, particularly from centrists who worry about pushing a divisive bill through an already divided Congress. With zero margin for error, a single Democratic senator or just a handful of House Democrats could force the party to change tactics.

Sen. Joe Manchin (D-W.Va.) — a moderate pushing for bipartisan talks rather than Democrats’ go-it-alone approach through reconciliation — said Biden has told him Democrats can’t afford to waste time by negotiating for months on end, only to ultimately pass their own package without GOP support.

“If it’s $1.9 trillion, so be it,” Manchin said on MSNBC’s “Morning Joe” Wednesday. “If it’s a little smaller than that and we find a targeted need, then that’s what we’re going to do. But I want it to be bipartisan, so if they think that we’re basically going to throw all caution to the wind and just shove it down people’s throats, that’s not going to happen.”

Senate Minority Leader Mitch McConnell said Republicans will be waiting with a “host of amendments” to the budget measure, including provisions on whether “taxpayers should fund checks for illegal immigrants” and whether “Democrats should raise taxes on small businesses.”

The budget measure that the House and Senate plans to pass this week directs a dozen committees to start pulling together Biden’s pandemic aid plan over the next two weeks, including $1,400 stimulus checks, $350 billion in state and local aid and more controversial provisions, like a $15 minimum wage hike.

Democrats, including Biden, have stressed that their plan has bipartisan support from Republican voters, if not GOP members of Congress.

“The question that remains is, ‘Will it be bipartisan here in the House and the Senate?’ And that’s for the Republicans to decide,” House Democratic Caucus Chair Hakeem Jeffries (D-N.Y.) told reporters Wednesday.

The Congressional Budget Office will soon release a report, at the request of incoming Budget Chair Bernie Sanders (I-Vt.), that makes a persuasive case for including the minimum wage boost in reconciliation legislation — all the pieces of which must have a significant impact on the federal budget.

But it’s unclear if that will be enough to sway centrist lawmakers like Manchin, who oppose the $15-an-hour wage increase.

Marianne LeVine and Burgess Everett contributed to this report.