ALBANY, N.Y. — Gov. Kathy Hochul has proudly displayed her credentials as a die-hard fan of the Buffalo Bills since taking office, posting photos of herself watching games and peppering her speeches with extemporaneous comments about her hometown football team.

But Ms. Hochul’s most consequential support of the Bills has unfolded in monthslong back-room talks with the team’s owners to build a $1.4 billion stadium.

The negotiations reflect the governor’s desire to keep the team in Western New York during an election year, as well as the state’s unusually rosy fiscal picture: Instead of facing billions of dollars in projected deficits, New York is currently awash in federal funds.

But giving a sports team a substantial government subsidy, which must be approved by state lawmakers, is still sure to provoke backlash from critics likely to denounce the deal as a boondoggle.

The new stadium is expected to be financed with up to $1 billion in taxpayer money, a combination of funding from the state and Erie County, where Buffalo is, according to two people familiar with the structure of the proposed deal, which still has not been finalized. The remainder of the construction costs, the people said, would be financed through a loan from the N.F.L. and money from the team owners.

With the state budget due next week, Ms. Hochul may be forced to explain the taxpayer benefits of spending on a new stadium, despite a long history of publicly funded arenas that have yielded little economic impact.

“If she were seen as the person that let the Bills leave, then she’s probably got a shelf life,” said Assemblyman Patrick Burke, a Democrat from Buffalo whose district includes the Bills’ stadium. “But if she’s also seen as someone who doesn’t drive a hard bargain and just gives away public dollars to billionaires, that’s going to be a problem for everyone, including me.”

There is also an immeasurable element to the equation: How much is it worth to retain a football team profoundly ingrained in the social fabric and cultural identity of a large swath of the state?

The Bills have been based near Buffalo, a postindustrial city on the shores of Lake Erie, since their founding over 60 years ago. The team relishes its standing as the only football team to play its home games in the state; the New York Jets and Giants play in New Jersey. (The Bills have also made the playoffs three straight years; the Jets and Giants have gone 22-59 in the last five years, tied for the worst in the league.)

But the owners of the Bills, Terry and Kim Pegula, say that the team’s current home, Highmark Stadium in nearby Orchard Park, is approaching the end of its useful life, despite the state helping to finance renovations there just eight years ago.

The Pegulas have also indicated that the franchise would not renew its current lease, which expires next year, and have instead sought public financing to cover most of the cost of a new stadium. Renovating the current stadium, the team and officials have agreed, would be almost as expensive as building a new one.

The proposed open-air stadium would fit over 60,000 fans, less than the current capacity, but would include more luxury club seating, which brings in far more revenue than regular seats. The stadium’s curved design would protect about 80 percent of the seats from the strong winds and snow that arrive in November and December. It could open as early as 2026 and would be located across the street from the current stadium, which is expected to be razed.

There is intense debate about whether the Pegulas, who bought the Bills in 2014, would actually relocate them if another city offered to spend more on a new stadium.

The editorial board of Syracuse’s main news outlet recently described any threat that the team would leave as a bluff, writing that, “Taxpayers should not be bullied into bailing out the team’s uber-rich owner and the uber-uber-uber-rich National Football League.”

Terry Pegula, who made his fortune through fracking, and also owns the Buffalo Sabres, an N.H.L. team, has a net worth of $5.8 billion, according to Forbes.

The N.F.L. has expressed support for building a new stadium in Western New York, as has Ms. Hochul, a Buffalo native and Democrat who took office in August following the sudden resignation of Gov. Andrew M. Cuomo.

The exact details of a potential agreement have remained elusive, including the split between funding from the state and county, how any bonds would be financed and who would be on the hook for any cost overruns.

Ms. Hochul has said she expected to have a deal in place before the April 1 deadline to finalize the state budget, saying last week that the negotiations were “right on track.”

“If the Bills left Western New York, it would be a devastating loss to the psyche and the fabric of our community, so losing the Bills is not an option,” said State Senator Tim Kennedy, a Democrat from Buffalo. “How we get there and how we finesse this through the budget process is something that I think still has to take shape.”

Ms. Hochul has yet to present a potential deal to state lawmakers, adding even more friction to already tense negotiations over other competing issues in the state budget, including new proposed funding for child care programs.

State Senator Liz Krueger, a top Democrat leading budget negotiations, said on Wednesday that she had only heard rumors of a state subsidy, telling reporters, “If any of you know, let me know.”

Public funding for stadiums has a long and contentious history in the United States.

Governments began subsidizing the construction of sports stadiums mostly after the 1950s, as cities and states started kicking in taxpayer dollars to keep professional teams from leaving, pitching the investments as a way to attract tourist dollars.

But many of these stadium deals turned into drains on the public coffers, and economic research has found that professional sports stadiums rarely have significant impact on overall economic growth.

“The public and lawmakers should both be given the information and the time to fully evaluate this,” said Patrick Orecki, a director of state studies at the Citizen Budget Commission, a fiscal watchdog.

In recent years, many New York sports teams, from the Yankees to the Mets, have largely paid for their own stadiums, though many venues have been built with public assistance in the form of free land, tax breaks and infrastructure improvements in the surrounding area.

Madison Square Garden in Manhattan has had a property tax exemption since 1982, while the Barclays Center in Brooklyn received $260.3 million in state and city funding, as well as property tax exemptions. The ballparks for the Yankees and the Mets received tax breaks and tax-free bonds, but the teams are paying off the bonds with revenue from their stadiums.

If taxpayers end up responsible for about $1 billion for a new Bills stadium, that would amount to over 70 percent of the estimated construction costs, which is in line with recent stadium deals in smaller markets across the N.F.L., according to an analysis by The Buffalo News. But the size of the subsidy remains on the high end, both in the state and across the nation.

In the last two N.F.L. stadium deals, public funding was less substantial. When the Rams moved to Los Angeles from St. Louis in 2016, the owner of the Rams paid entirely for the team’s new stadium in Inglewood, Calif. But when the Raiders moved to Las Vegas from Oakland, Calif., in 2020 for a $2 billion stadium, Clark County in Nevada contributed $750 million in bonds backed by hotel receipts.

While the financing terms for a Bills deal remain unclear, some have argued that a large state subsidy is necessary because Buffalo is one of the smallest markets in the N.F.L., meaning it doesn’t have the collection of big corporate sponsors that pay top dollar for stadium naming rights, luxury boxes and season tickets.

The league also has little desire to abandon Buffalo: The N.F.L. commissioner, Roger Goodell, grew up in Western New York, and other team owners recognize the team’s value as similar to Green Bay’s storied Packers — a kind of civic underdog with a compelling story line.

There are other moving pieces at play.

A loan of roughly $200 million from the N.F.L. would be contingent on the team having at least a handshake deal with the state. The league owners could consider a conceptual deal during league meetings that begin on Sunday in Florida, but they could also approve the loan later this year.

Pegulas Sports and Entertainment, which owns the stadium, would also pitch in private money, likely by selling personal seat licenses to fans to help fund the construction.

Erie County would own the stadium and would also facilitate financing that would have to be approved by the county’s legislature.

A spokeswoman for Ms. Hochul, Julie Wood, cautioned that the deal had not yet been finalized. “Any reports of details are premature,” she said. “As we have said repeatedly, negotiations are ongoing.”

But Mark C. Poloncarz, the county executive, who is involved in the negotiations, put a more positive spin on the talks, saying on Wednesday that “very soon we’ll be able to announce that we have a signed deal, and here are the terms.”