WASHINGTON — President Biden and Sen. Joe Manchin are sharply divided over Democrats’ huge social and environment bill, with the holdout senator pushing to erase the measure’s improved child tax credit, a person familiar with the talks said Wednesday as leaders’ hopes of passing the legislation before Christmas appear increasingly bleak.

The rocky status of the talks, described by a person only on condition of anonymity, were among the indications that Senate Majority Leader Chuck Schumer faces a struggle just to begin debate on the massive measure before the holiday. Schumer, D-N.Y., has set a goal for passage of the 10-year, roughly $2 trillion measure by Christmas, in hopes of finally concluding his party’s eight-month push.

Letting work on the legislation slip into next year, when congressional elections will be held, would be an ominous sign about its prospects. That delay would also deal a blow to a party bracing for November elections, when Republicans have a real chance of winning control of the House and Senate.

Sen. Joe Manchin, D-W.Va., walks to a vote in the Senate Chamber on Wednesday in Washington. Jacquelyn Martin/Associated Press

Manchin told reporters that assertions he opposes that tax credit were “a lot of bad rumors,” adding that he has “always been for child tax credits.” Asked if he backed the legislation’s continuation of monthly tax credit checks sent to millions of families, he said, “I’m not negotiating with any of you.”

Democrats need all their votes in the 50-50 Senate to advance the legislation. Unresolved disputes with Manchin and other time-consuming hurdles have made it seem increasingly unlikely that senators could even begin debating the bill before the holiday. The bill is a top priority for Biden and the party.

Many Democrats consider the expanded child tax credit crucial for the millions of families it helps and for the legislation’s prospects of moving through the narrowly divided Congress. The measure also has money for health care, universal prekindergarten and climate change programs.

“It would be a disaster for working families and parents in this country,” Senate Budget Committee Chairman Bernie Sanders, I-Vt., said of the consequences if the child tax credit fell from the bill.

According to senators and aides, Schumer has not said he is planning to delay work on the bill into next year. But many obstacles must be cleared before the bill can come to the floor, let alone be approved.

Schumer must reach agreements with Manchin over his demands to curb the legislation’s price tag and remove provisions he opposes, such as required paid family leave and some tax credits for clean energy. There are other disputes as well, including how to increase federal tax deductions for state and local taxes.

The Senate’s parliamentarian still has to consider whether many provisions abide by the chamber’s rules and should remain in the legislation. These include a Democratic effort to help millions of immigrants stay temporarily in the United States.

Schumer has scheduled the Senate to be in session the week of Jan. 3, potentially creating time for lawmakers to plunge quickly back into work on the bill. Congress is seldom in session in early January in election years.

Biden and Manchin have spoken by phone about the legislation at least twice this week. White House deputy press secretary Karine Jean-Pierre on Wednesday said they were “great conversations” that have been “productive.”

Schumer sidestepped a question by reporters on Tuesday about whether he thinks Manchin wants the overall bill approved. “Sen. Manchin’s having good discussions with the president, as I said, and we’re doing all of the things we have to do to get it in play,” Schumer said.

The House approved its version of the legislation in November.