Last week, the self-described Democratic socialist held two media events and stepped up his criticism of Mr. Manchin and Ms. Sinema. He told reporters that the centrists needed to be clear about what they wanted—and that the entire party shouldn’t have to move all the way to them.

“I am delighted that the Democratic caucus and the president are prepared to think big and not small,” Mr. Sanders said in an interview with The Wall Street Journal. Of the centrists, he said: “They have a right to fight for their ideas, they have a right to get concessions for their ideas, as does every other member of the caucus, but it does seem to me to be basically unfair and undemocratic for two people to say it’s my way or the highway.”

Mr. Manchin has said he would like to see the package cost $1.5 trillion, while Ms. Sinema hasn’t shared any number publicly. After initially backing $3.5 trillion, President Biden has begun floating a roughly $2 trillion level as a compromise.

Democrats are using a special budget maneuver to pass the legislation without any Republican support, but they need all 50 lawmakers to remain on board. Any one senator’s opposition would sink the bill. Much of the party’s focus has been on winning over Mr. Manchin and Ms. Sinema, but Mr. Sanders must also decide what he is willing to accept and how hard he will push for it. So far, he says that number is still $3.5 trillion.

As Mr. Sanders says he is holding firm, other liberals are acknowledging they will need to accept less. Rep. Pramila Jayapal (D., Wash.) who chairs a group of House progressives, told President Biden a package needed to be at least $2.5 trillion.

“At some point, all 50 of us are going to have to vote on the bill,” said Sen. Mazie Hirono (D., Hawaii).

Mr. Sanders, an independent, was once on the fringe of the Democratic caucus. But his two runs for president popularized within the party a larger role for government in the economy, paid for by higher taxes on wealthy households and big business. While some signature goals, such as a Medicare for All healthcare system, remain sidelined, the current Democratic proposal has embraced or moved toward other of his ideas, including free preschool and subsidized child care, more-affordable housing and provisions to mitigate climate change.

To fund the programs, Democrats say they plan to raise taxes on corporations, investors and high-income business owners, with the size of the tax increases potentially being scaled back if the spending plans are narrowed. The details remain in flux. Mr. Sanders and Democrats have said they expect new revenue to cover the full price of the package.

No Republicans are expected to vote for the package, whatever its eventual size. They have termed the plan a reckless spending proposal that could hurt the economy.

“This is a 50-50 body,” said Sen. Ted Cruz (R., Texas) on the Senate floor. “And yet Democrats have interpreted this incredibly close election as a mandate to radically transform this country,” calling their spending plan the “Bernie Sanders socialist budget.”

Rep. Ro Khanna (D., Calif.), a liberal who is close to Mr. Sanders, said Messrs. Sanders and Manchin need to engage in direct talks. If they can agree, Mr. Khanna said, the rest of the Democratic Party will follow.

“He’s the standard bearer of the progressive movement. Once he signs off on something, every progressive in the House will vote for it,” Mr. Khanna said about Mr. Sanders.

Mr. Sanders has declined to say if he has been talking to Mr. Manchin or Ms. Sinema. When he was asked by a reporter Friday if it made sense to just get in a room with the centrists to hash out a deal, he quipped: “It’s not a movie.”

A spokesman for Ms. Sinema declined a request for comment.

A spokeswoman for Mr. Manchin pointed the Journal to a statement Mr. Manchin had made last week after Mr. Sanders criticized him in a news conference.

“As he and I have discussed, Sen. Sanders believes America should be moving towards an entitlement society while I believe we should have a compassionate and rewarding society,” Mr. Manchin said in his statement.

As one way to cut costs, Mr. Manchin has signaled support for means-testing of some programs to target lower-income Americans rather than make them available to all. Mr. Sanders said he isn’t thrilled by that idea. Proponents have floated making two free years of community college available only to low-income Americans, or reducing the income cutoffs for the child tax credit.

Passage would secure a major piece of Mr. Biden’s busy first-year agenda, adding trillions of dollars in spending on top of a $1.9 trillion Covid-aid package and a $1.2 trillion bipartisan infrastructure bill pending in Congress.

​“My message is simple, we need to stay together,” Mr. Biden said during video remarks at the Democratic National Committee fall meeting Saturday.

Mr. Sanders maintains the current package can’t get smaller and that he has already compromised. As chairman of the Budget Committee, which is helping to draft the legislation, Mr. Sanders had originally proposed a $6 trillion package but came down to $3.5 trillion in order to get the support of committee members Mark Warner and Tim Kaine, both of Virginia. Much of the cost cuts came from shortening the proposed duration of programs.

Tensions with centrists have been on display in other ways. Mr. Sanders declined to sign onto a statement from Democratic leadership condemning protesters who followed Ms. Sinema into a bathroom, because it didn’t include his office’s suggested edit urging her to support the spending package. The email exchange was reported by Axios.

“I think a letter which does not acknowledge the importance of what Lucha is doing and why they are protesting Sen. Sinema would be incomplete,” he said of the Arizona bathroom incident. Lucha, for Living United for Change in Arizona, is a progressive advocacy group that has been critical of Ms. Sinema.

Some voters who supported Mr. Sanders for the Democratic presidential nomination last year said they want as large a package as possible but also understand the realities on Capitol Hill. Senate Democrats can’t lose a single vote, and House Speaker Nancy Pelosi (D., Calif.) can lose only three members in her chamber.

Stephanie Grohs, a 63-year-old retired college librarian from Napa, Calif., said she is uncomfortable with a $2 trillion package, but understands if Mr. Sanders and progressives need to come down from $3.5 trillion

“I don’t think he should hold the line in the sand” at $3.5 trillion, she said about Mr. Sanders. “I never thought I’d say that because I’m kind of idealistic, but these are tough times.”