In a sign of possible momentum, Senate Majority Leader Charles E. Schumer (D-N.Y.) wrote to lawmakers Friday that the upper chamber could consider the bill — along with measures to regulate TikTok, address rail safety and lower health-care costs — “in the weeks and months ahead.”

Once the Senate wraps up impeachment proceedings against Homeland Security Secretary Alejandro Mayorkas, expected to take up most of lawmakers’ time next week, Schumer could put the tax bill to a vote on or shortly after the April 15 tax deadline.

The $79 billion legislation pairs an expansion to the child tax credit — a major priority for President Biden and Democrats that nonpartisan estimates say would lift 400,000 children out of poverty — with business tax incentives initially authorized in 2017 under President Donald Trump.

The Internal Revenue Service has said it could apply the credit retroactively, but lawmakers have still been eyeing the filing deadline as a possible time peg for action on the measure.

It was the product of a deal struck between Sen. Ron Wyden (D-Ore.) and Rep. Jason T. Smith (R-Mo.), the chairs of Congress’s tax-writing committees, after seven months of talks, and it passed the House with broad bipartisan support in January.

The bill has run into opposition from Sen. Mike Crapo (Idaho), Wyden’s Republican counterpart on the Finance Committee, over a provision that would allow low-income families to use a prior year’s return to earn a larger tax credit. Many Republicans have publicly followed Crapo’s lead, hoping to give him more leverage to seek changes to the legislation that dial back the credit for families.

Privately, though, numerous Republican senators say they could support the legislation without some of those changes, but don’t want to outwardly break with a well-liked and powerful member of their caucus, the four people who have discussed the measure with them said.

These people — three lobbyists and a senior GOP Senate staffer who have had in-depth conversations with lawmakers and senior staffers about the bill — said that in private, a sufficient number of Republicans to overcome a filibuster support the legislation, but many of them do not want to cross Crapo and other GOP leaders who hope to extract more concessions from Wyden and Smith.

“The thing that we see differently now is there does not seem to be the willingness that anyone is going roll Crapo,” one of those people said. “That’s pretty clear from Republicans now. We see that the path forward for this bill is that concessions need to be made.”

A left-leaning advocacy group had a similar read.

“We’ve had conversations with over a dozen Republican Senate offices and heard significant support for the bipartisan tax package and enthusiasm both for the [research-and-development] credit as well as for the child tax credit provision,” Adam Ruben, director of Economic Security Project Action. “I would predict that if this comes to a vote, I think the votes are there. … Will it come to a vote [and overcome a GOP filibuster threat] is another question.”

Wyden offered to alter the legislation to address some of Crapo’s concerns, swapping out the “look back” section and instead further expanding eligibility for the poorest families who qualify for the credit. Crapo rejected that offer: He has said negotiations with Wyden were “at a standstill.”

“The issue set is the same issue set that’s been out there for a couple of weeks now,” Crapo told The Washington Post before Congress went on recess at the end of March.

Ultimately, public support for the bill hinges on Crapo’s stance in negotiations, the people and multiple lawmakers said. Lawmakers say Crapo, who is in line to chair the Finance Committee if Republicans retake the Senate in November’s elections, is eyeing a larger tax package in 2025 that could contain more conservative policies and hopes to use the prospect of a GOP-written tax plan next year to extract more changes from Wyden — or defeat the measure entirely.

Trillions of dollars in tax cuts enacted under Trump are slated to expire at the end of 2025, which means Congress will probably be working on tax policy next year regardless of who wins the elections.

“I think Crapo wants to make it better,” Sen. Lindsey Graham (R-S.C.) said. “I like to help people raising children with the child tax credit, and there’s a bunch of other business things in there that I hear a lot about from my constituents. But with work requirements, there’s some things that Crapo wants to do and I sort of trust his judgment.”

Another key Republican, Sen. Mike Rounds (S.D.), echoed that sentiment.

“I have spoken with our ranking member, Mike Crapo, and I don’t think it’s ready for prime time yet,” Rounds said. “I think they’re still negotiating. But I’ll take my cue right now based on what his analysis is.”

Wyden is still offering to drop the ability for taxpayers to use a previous year’s return to quality if it will draw Republicans on board.

“While I think the policy is important, I’ve offered to take it out of the bill if it gets this over the finish line,” he said during a committee hearing in late March. “Working with groups, we have found a way to do this and still lift the same number of kids out of poverty. As of this morning, my offer on the look back is still on the table.”

Some key Republicans hope Wyden succeeds. A high-profile Finance Committee member, Sen. Todd Young (R-Ind.), urged Senate leaders to move forward even if Crapo cannot secure more changes to the legislation. And a member of GOP leadership, Sen. Steve Daines (Mont.), has said the bill even without changes was “very important for global competitiveness” because of the corporate tax provisions.

The new legislation would expand the child tax credit to allow low-income families to claim the benefit for multiple children; under current law, the lowest-earning families can only receive the credit for one child. Starting in 2025, for the 2024 tax year, the benefit would be linked to inflation, which would add up to a roughly $100 boost next year.

The proposed larger refundable tax credits for more low-income parents could lift 400,000 children out of poverty, according to nonpartisan estimates. And Democrats and Republicans alike have cheered provisions that would allow businesses to write off research-and-development and interest expenses and investments in new equipment.

The tax credit was expanded temporarily in 2021, increasing the amount it provided and extending eligibility. Those changes kept 3 million children out of poverty, according to research conducted by Columbia University’s Center on Poverty & Social Policy. But the expansion expired at the end of 2021, and child poverty rates jumped back up after that.