WASHINGTON — With pressure mounting but signs of progress, President Biden will hunker down at the White House to try to strike a deal and win over two holdout Democratic senators whose support is needed for his potentially historic $3.5 trillion government overhaul.

With Republicans solidly opposed and no Democratic votes to spare, Biden canceled a trip to Chicago on Wednesday that was to focus on COVID-19 vaccinations so he could dig in for another day of intense negotiations with lawmakers before crucial votes.

The stakes are as high as ever as Biden and his party try to accomplish a giant legislative feat, promising a vast rewrite of the nation’s balance sheet with an oh-so-slim majority in Congress. His idea is to essentially raise taxes on corporations and the wealthy and use that money to expand government health care, education and other programs — an impact that would be felt across countless American lives.

As if that wasn’t enough, Biden’s focus is gaining traction at the same time Congress courts a crisis. Republicans refuse to approve routine legislation to keep the government funded past Thursday’s fiscal year-end and raise the nation’s debt limit to avoid a dangerous default on borrowing. More votes are expected Wednesday and are likely to at least temporarily head off a catastrophe.

With Biden and his party reaching for what would be a signature policy accomplishment, there is a “strong sense” that progress is being made, said an administration official who requested anonymity to discuss the private talks.

All eyes are on Sens. Joe Manchin of West Virginia and Kyrsten Sinema of Arizona, who say the price for Biden’s plan is too big but are publicly quiet about a number they can accept.

The president met separately with the two centrist senators at the White House on Tuesday and Democrats are poised to trim the huge measure’s tax proposals and spending goals to meet the overall size they are demanding.

“Really good, honest, straightforward negotiations,” Manchin told reporters back at the Capitol after his White House meeting with Biden. He said he did not give the president a new topline figure.

Biden’s problems with fellow Democrats aren’t just in the Senate. A small number of centrist House Democrats are bristling at the far-reaching scope of his domestic agenda and demanding changes. But progressive lawmakers warn against cutting too much, saying they have already compromised enough.

Applying pressure, progressives are threatening to withhold support for a companion bill, a $1 trillion public works measure heading to a vote Thursday, that they say is too meager without Biden’s bigger package assured.

“We’re obviously at a very sensitive time,” said White House press secretary Jen Psaki. The president, she said, is “not going to tell anyone what to do. He’s going to have a discussion, have an engagement.”

Taken together, it’s all putting the entire Biden agenda perilously closer to collapse, with consequences certain to shape his presidency and the lawmakers’ political futures.

Treasury Secretary Janet Yellen told Congress in a letter Tuesday that Oct. 18 is a critical date — the day the Treasury Department will likely exhaust all of its “extraordinary measures” being taken to avoid a default on the government’s obligations.

Yellen urged Congress to “protect the full faith and credit of the United States by acting as soon as possible” to either raise the debt limit or suspend it.

Faced with Republican opposition to linking the routine government funding with the debt limit vote, Democrats are separating the two, stripping out the more-heated debate over the debt limit for another day, closer to a separate October deadline.

The Senate is poised to vote swiftly to provide government funding to avoid a federal shutdown after the Sept. 30 fiscal year end, keeping operations flowing temporarily to Dec. 3. The House could quickly follow.

The House is also preparing a possible vote to extend the debt limit through through Dec. 16, something Democrats are likely to support. But even if it is approved by the House, it’s unclear if it could pass the Senate in the face of GOP obstruction.

Tensions are flaring at the Capitol as the contours of Biden’s big agenda come into focus amid standoff over normally routine votes over government operations.

Senate Republican leader Mitch McConnell grew testy with reporters when asked about Yellen’s warning that Congress must swiftly resolve the issue.

“Of course the debt ceiling has to be raised,” McConnell said. But he insisted Democrats shoulder the unpopular vote on their own.

Meanwhile, the behind-the-scenes action over the $3.5 trillion measure is testing Biden’s grip on his party, as he seeks a once-in-a-generation reworking of the nation’s tax priorities and spending goals.

With all Republicans opposed to the big bill, Democratic leaders can’t spare a single vote in the 50-50 Senate, relying on Vice President Kamala Harris to break a tie to pass the eventual package.

Physically holding up the bill of 2,000-plus pages, Republican Sen. John Barrasso of Wyoming warned it was nothing but “big government socialism.”

Biden insists the price tag actually will be zero because the expansion of government programs would be largely paid for with higher taxes on corporations and the wealthy — businesses earning more than $5 million a year, and individuals earning more than $400,000 a year, or $450,000 for couples.

To lower the price tag and win over centrist Democrats, it’s not necessary that any specific programs be get axed, those familiar with the process have said. Rather, lawmakers are eyeing ways to adjust the scope and duration of some of Biden’s proposals.

Still, Rep. Pramila Jayapal, D-Wash., the chair of the Congressional Progressive Caucus, said they have the votes to derail the other bill unless it comes with Biden’s broader one — tacit pressure on the holdouts to arrive at a deal. Backing that position, Sen. Bernie Sanders, I-Vt., also urged a no vote.