Joe Biden’s domestic agenda continued to hang in the balance on Monday, as the president and Democratic leaders sought to pull their party together and deliver the biggest overhaul of government priorities in decades.

From the White House, Biden continued to speak with lawmakers. After receiving a Covid-19 booster shot, he told reporters: “We’ve got three things to do: the debt ceiling, continuing [government funding] resolution and the two pieces of legislation.”

In Congress, Democratic leaders looked at ways to trim back the $3.5tn price tag of one of those pieces of legislation, Biden’s tax and spending package, in order to win over remaining lawmakers while working to avoid a government shutdown and a debt default.

With the House due to convene only in the late afternoon, a vote on the second piece of legislation, a bipartisan $1tn infrastructure bill, was expected on Thursday.

“We do [all] that,” Biden said, “the country is gonna be in great shape.”

The Senate had a test vote set for Monday, on a combined measure to keep the government funded past Friday and avert an unprecedented debt default.

The measure stood to be blocked by Republicans, who have refused to vote with Democrats on the debt ceiling despite Democrats doing so under the Trump administration, a time when Republican tax cuts added to the national debt.

In a letter released to reporters, the House majority leader, Steny Hoyer, and 63 other Democrats accused Mitch McConnell, the Republican leader in the Senate, of “manufacturing a crisis” and said: “Holding the debt limit hostage is … dangerous, illogical and irresponsible.”

Biden, the House speaker, Nancy Pelosi, and the Senate majority leader, Chuck Schumer, remained deep in negotiations over the spending proposal, which was being chiseled back from $3.5tn to win over moderate senators and House lawmakers who have refused the price tag and tax increases on corporations and the wealthy to pay for it.

Democratic moderates and progressives are at odds over whether the spending package or the infrastructure deal should be given priority. Pelosi announced the Thursday vote on infrastructure in a letter late on Sunday.

The Democrat Josh Gottheimer of New Jersey, who led House moderates in a securing the vote on the infrastructure bill, said on Sunday he was optimistic both pieces of legislation could be resolved this week.

Biden’s spending plan would provide an expansion of existing health, education and childcare programs alongside new federal efforts to curb climate change. But it must pass via reconciliation, a budgetary measure which means a simple majority is needed.

Republicans are uniformly opposed to Biden’s proposal, which would be paid for by increasing the tax rate on businesses earning more than $5m a year and raising the top rate on individuals from 37% to 39.6% for those earning more than $400,000, or $450,000 for couples.

In the Senate, Democrats are under pressure. The chamber is split 50-50, with Vice-President Kamala Harris as the tiebreaker vote. Two Democratic moderates, Joe Manchin of West Virginia and Kyrsten Sinema of Arizona, have said they won’t support a $3.5tn spending bill. Manchin has proposed $1tn to $1.5tn.

Asked on Sunday on ABC if the final number on the bill would be “somewhat smaller” than $3.5tn, Pelosi said: “That seems self-evident.

“We’ll see how the number comes down and what we need,” she said. “I think even those who want a smaller number support the vision of the president and this is really transformative.”

Pelosi and Schumer face the toughest challenge of their careers in Congress. While progressives say they have compromised enough on Biden’s big bill, having come down from $6tn, some are acknowledging more potential changes. On Sunday, Pramila Jayapal of Washington state, who heads the Congressional Progressive Caucus, didn’t rule out additional cuts.

“If somebody wants to take something out, we need to hear what that is,” she told CBS.

Pelosi suggested agreement could be reached this week, depending on rulings from the Senate parliamentarian. But stubborn differences remain. Among them are splits over which initiatives should be reshaped, including how to push toward cleaner energy or to lower prescription drug costs.

Republicans say the proposal isn’t needed and can’t be afforded given federal debt exceeding $28tn. They also argue that it reflects Democrats’ drive to insert government into people’s lives.