WASHINGTON—Democrats are grappling with the fiscal and political limits of their pursuit of a broad antipoverty and climate bill, with some senior lawmakers preparing to slim down or eliminate elements of the proposal as moderates push to shrink the $3.5 trillion package.

Senators return to Washington Monday after a weekslong break, in a rush to craft the legislation at the center of President Biden’s agenda, an effort that Republicans oppose. To pass the bill with just Democratic votes, lawmakers will need to navigate a host of intraparty disagreements over the legislation—which aims to expand access to child care, education and healthcare while also raising taxes on high-income households and companies.

At the same time, lawmakers also face looming deadlines on annual government funding, which is currently set to expire on Oct. 1, and the government’s debt limit. Treasury Secretary Janet Yellen has warned lawmakers that the government could exhaust its ability to pay its bills on time in October if Congress doesn’t authorize additional borrowing. 

The pileup of big-ticket topics is set to create a potentially chaotic few weeks on Capitol Hill, where Democrats confront divisions both within their own ranks and with the GOP. Moderate Democrats are pushing to pare back the spending in the bill, raising concerns about both the size of the tax increases and possible borrowing needed to cover its cost. Democrats can’t afford to lose any votes in the Senate or more than three in the House.

“The hard part will be how to pay for it, what are the offsets. That may prove to be a constraining element to how big the package is at the end of the day,” said Rep. Ron Kind (D., Wis.), a member of the tax-writing House Ways & Means Committee.

Rep. Ron Kind (D., Wis.) is one of the legislators looking for ways to fund the antipoverty and climate package.

Photo: Bill Clark/Zuma Press

Democrats are studying a range of revenue measures—including raising the corporate tax rate, raising the top income-tax rate, enhancing tax enforcement and raising the top capital-gains rate—to finance the package. But some of those proposals, including taxing unrealized capital gains at death, have proved controversial among Democrats, while the extent of others, like raising the corporate rate, will likely be pared back before they come for a vote.

Sizing down the package would likely prove challenging for top Democrats, who are already dealing with the difficulty of squeezing in many of the party’s priorities into the $3.5 trillion plan. Some Democratic aides expect the bill’s spending to ultimately decrease amid opposition to the price tag from some key lawmakers.

Sen. Joe Manchin (D., W.Va.) reiterated on Sunday that he would refuse to vote for a $3.5 trillion package. “He will not have my vote on $3.5 [trillion] and Chuck knows that,” Mr. Manchin said Sunday on CNN’s “State of the Union,” referring to Senate Majority Leader Chuck Schumer (D., N.Y.). Mr. Manchin noted the more than $5 trillion in federal spending Congress has already authorized in rounds of aid related to the coronavirus pandemic and said he was concerned about rising levels of debt and inflation.

One strategy Democrats are eyeing to address the priorities of the party’s various wings, while also staying with their budget, is to fund some priorities for the short term, leaving their long-term fate in the hands of future Congresses.

Senate Majority Leader Chuck Schumer, in New York City last week, and other Democratic lawmakers could trim or limit some provisions of the $3.5 billion package.

Photo: Ron Adar/Zuma Press

“In general, we would like to make all of these things permanent, but obviously the $3.5 trillion puts in some constraints. And so not everything is going to be as long as we’d like it for,” Mr. Schumer said during a press event last week.

Democrats are deciding on how long to fund an enhanced child tax credit, which Democrats expanded as part of the $1.9 trillion coronavirus relief law earlier this year. That law increased the size of the credit for many families, along with making it fully refundable and available in regular payments through 2021.

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Democrats are hoping to extend that expansion into future years but share differences over how many resources in this bill to dedicate to that expansion, with some lawmakers pushing for making it permanent. House Democrats want to extend the new benefits through 2025, while Senate Democrats are looking at an extension through 2024, according to an aide.

Rep. Suzan DelBene (D., Wash.), chairwoman of the New Democrat Coalition, a centrist bloc in the House, said Democrats should focus funds on a smaller number of priorities like the child tax credit. New Democrats have been advocating for extending the expansion of the child tax credit through at least 2025.

“We need to make sure we focus on doing really important things well, those few things really well, and the child tax credit is definitely one of those things,” she said. “We want to make sure that we don’t have a litany of programs that are sunsetting.”

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Progressive Democrats are fighting to keep the bill’s top line at $3.5 trillion, an effort that will intersect with the fate of the $1 trillion infrastructure bill that the Senate passed with bipartisan support earlier this year. Progressives in the House have said they would withhold their support for the infrastructure bill until the $3.5 trillion bill clears the Senate, while moderates have pushed for the infrastructure bill to receive a vote first.

Sen. Bernie Sanders (I., Vt.) said there was a possibility that neither bill passes if neither Mr. Manchin moves off his position to pass the infrastructure bill first nor progressive lawmakers move off their position to move the two pieces of legislation simultaneously.

“That is a possibility, and I think that would be a disaster for the American people,” he said in an interview Sunday on ABC’s “This Week.” “There is a real danger the infrastructure bill will lose in the House.”

To defuse a threat from a group of moderate House Democrats to vote against the initial budget outline for the $3.5 trillion bill last month, House Speaker Nancy Pelosi (D., Calif.) said that the House would take up the infrastructure bill by Sept. 27. That deadline has added to the time crunch in Congress, creating the potential for another showdown among Democrats if the climate and antipoverty bill is still in the works at that time.

—Ted Mann and Nick Timiraos contributed to this article.

Write to Andrew Duehren at andrew.duehren@wsj.com