President Biden told Democrats during a private meeting Tuesday that he believed they could secure a deal on a new tax-and-spending proposal between $1.75 trillion and $1.9 trillion, far less than some in the party initially sought, even as some lawmakers later maintained it still would allow them to accomplish broad swaths of their vast economic agenda.

The early outline — shared at least with liberal lawmakers in the House — appeared to offer one potential avenue for the White House to broker a truce among Democrats’ warring left-leaning and moderate factions. Four people familiar with Biden’s comments confirmed the early details, requesting anonymity to describe the negotiations.

The potential new price range marks a significant reduction from the $3.5 trillion that some Democrats initially pursued under a budget agreement chiefly brokered by Sen. Bernie Sanders (I-Vt.) earlier this year. But it is closer to the number that centrists, especially Sen. Joe Manchin III (D-W.Va.), had outlined in recent months as they sought steep cuts to Democrats’ spending plans. Manchin and Sanders met Tuesday for the second time in two days after the two sparred with each other over the weekend.

By the White House’s calculations, a package up to $1.9 trillion would allow them to accomplish some of their most significant priorities. That includes at least some expansion of Medicare to offer new benefits to seniors, the introduction of universal prekindergarten, and billions of dollars to address climate change, the sources said, cautioning that many of the details must still be worked out.

President Biden traveled to Michigan on Oct. 5 to build public support for his economic plans. (The Washington Post)

But slimming down the package also is sure to force Democrats to make some sacrifices. The path put forward by the White House could extend new, expanded child tax credit payments recently adopted by Congress, but perhaps for only one additional year, three of the sources said. It would offer new money to make housing more affordable, yet far less than Democrats once envisioned. And it would provide paid leave, except only four weeks of benefits, rather than the 12 weeks some had once proposed, according to one of the people in the room.

Some congressional sources cautioned that many of the ideas aired by the White House remain in flux, reflecting considerable work still on the horizon to craft a deal and sell such a scaled-back package to an increasingly fractious Democratic caucus. Biden also did not broach the issue of how to finance the new spending, leaving unresolved the fight over his proposal to raise taxes on wealthy Americans and corporations. He previously pledged it would be paid for in full.

The White House on Tuesday evening did not immediately respond to a request for comment. Earlier in the day, however, White House press secretary Jen Psaki described the meeting with liberals — and a second, separate session with moderate Democrats — as “constructive” toward potentially reaching a deal after months of delays.

“There was broad agreement that there is urgency in moving forward over the next several days and that the window for finalizing a package is closing,” she said in a statement.

Liberal-leaning Democrats, meanwhile, offered some early praise for what they heard Tuesday. They acknowledged some of the cuts while stressing that many of their policy priorities in health care, education and social spending appear to remain intact.

“All our priorities are there in some way, shape or form,” said Rep. Pramila Jayapal (D-Wash.), the leader of the Congressional Progressive Caucus.

The early outlines of a deal came on a day when Democrats pledged to muscle past the political sniping and policy feuds that have ensnared Biden’s economic agenda for months.

“There was universal, universal agreement in that room, that we have to come to an agreement, and we got to get it done and want to get it done this week,” Senate Majority Leader Charles E. Schumer (D-N.Y.) said earlier in the day, a lengthy party lunch he later described as “spirited.”

“The pace has picked up,” Schumer said. “The desire to get it done is strong.”

The proposal’s price tag had remained a major point of contention. Sanders and Jayapal had sought as much as $3.5 trillion over 10 years as they worked to expand Medicare benefits, invest new sums to combat global warming, and extend paid leave and tax credits to workers and families. But two key centrists, Manchin and Sen. Kyrsten Sinema (D-Ariz.), objected to the overall cost and vast policy scope favored by their liberal counterparts.

The standoff at times has proven acrimonious, pitting lawmakers like Sanders and Manchin against each other in a public war of words. Manchin specifically has pushed for a package closer to $1.5 trillion, forcing left-leaning members to make what they regard as unacceptable concessions.

Seeking to bridge the gap, Biden began Tuesday by meeting with Jayapal and other lawmakers. Exiting the discussion at the White House, Jayapal said she felt “very good” that the “majority” of the programs backed by the left-leaning bloc would be in the final deal.

“The president is the inspirer, he is the closer, he is the convincer, the he is the mediator-in-chief. He really is doing a phenomenal job,” she said.

Jayapal and other members of her bloc said that there is still hope for a final package to include an expansion to Medicare to cover dental, vision and hearing benefits as well as a new program that provides universal prekindergarten for children. Other sources later said that Biden had signaled other critical health care programs, including some money for elder care, extended insurance tax credits and fixes to Medicaid also remain in the mix.

But liberals also acknowledged there are likely to be some cuts, including the potential elimination of a proposal that would have provided universal free community college. Instead, Democrats appear to be eying a different proposal that might provide more limited scholarships, according to two of the sources.

One White House official, who also spoke on the condition of anonymity to describe the private meeting, stressed that the narrower legislation would still include major investments across a range of additional policy areas — including less-discussed initiatives for maternal health and Historically Black Colleges and Universities.

Biden and top Democrats also are still pursuing significant spending to address climate change, though Jayapal and others acknowledged their deal appears unlikely to include a program that would have paid utilities that switch to clean energy and penalized those that do not. Discussions on an alternative continue, she and other lawmakers said Tuesday, as liberals seek to overcome Manchin’s opposition to the program.

Some of the potential cuts did appear to frustrate liberal lawmakers. Biden’s new plan appeared to some in the room to underestimate the cost of expanding Medicare, raising questions as to how much more Democrats might have to scale back their other ambitions, according to two sources in the room. A stern Rep. Jared Huffman (D-Calif.), meanwhile, later urged Biden not to “give up” on a signature climate initiative simply in the face of Manchin’s opposition.

And Rep. Ritchie Torres (D-N.Y.), who represents the poorest congressional district in the country as measured by median income, said that he had stressed to Biden the importance of the child tax credit, which Torres pointed to as the “greatest triumph of racial equity.”

“I conveyed to the president that my two highest priorities are the child tax credit and affordable housing,” Torres (D-N.Y.) said in an interview. “And I quoted the great philosopher Jimmy McMillan, who said the rent is too damn high. We can’t build back better if the rent is too damn high.”

At the Capitol, meanwhile, Senate Democrats emerged from their own private lunch Tuesday expressing a sense of optimism about their ability to secure a new framework this week. But it remained unclear exactly how detailed such a deal might be, and how close the full caucus — including Sinema, a centrist holdout who did not attend the session — is to backing it.

“Closer than you think,” Sen. Thomas R. Carper (D-Del.) said Tuesday about the broader Democratic caucus. “What do they say about looking in your rearview mirror. … The object may be closer than you think. This is definitely doable. I am encouraged.”

The flurry of activity foreshadows what could be a frenetic, final sprint to end the year. Time is running out if lawmakers hope to deliver on Biden’s economic agenda before 2022, when the fight over fiscal issues could grow even more intense entering a midterm election year that will determine control of Congress in the final half of Biden’s first term.

Sensing the electoral stakes, the president is set to hit the road Wednesday, visiting Scranton, Pa., his birthplace, to pitch voters again on his vision. Previewing the trip, Psaki said Biden intends to “talk about growing up in Scranton and the way his experience there influenced his values and his belief that we need an economy that works for working people.”

The president has put his full political weight behind two separate but related packages. The first is a bipartisan, roughly $1.2 trillion plan to improve the nation’s roads, bridges, pipes, ports and Internet connections, which cleared the Senate earlier this year. The second is a broader, still-forming tax-and-spending package that Democrats hope to adopt using a legislative tactic that allows them to sidestep a Republican filibuster.

Politically, it appears neither legislative effort can advance without the other. Liberals have held up the infrastructure bill to maximize negotiations over additional spending, but they cannot advance that second package without centrists’ support. With only slim voting majorities, Democrats have no room for error in the face of sustained Republican opposition, which GOP lawmakers reiterated in clear terms Tuesday.

“Every day, American families are feeling real pain because of the reckless and inflationary policies that Democrats have already rammed through,” Senate Minority Leader Mitch McConnell (R-Ky.) said during a speech on the chamber floor.

Mike DeBonis contributed to this story.