Massachusetts has a nearly $5 billion surplus. Now what?

State officials project Massachusetts will have a nearly $5 billion surplus from the fiscal year that ended in June, offering policymakers a huge pot of cash to cover a likely multibillion-dollar refund due back to taxpayers.

Whether it also prompts lawmakers to reconsider shelving a wide-ranging tax relief package is another matter.

The surplus estimate, announced late Thursday by Governor Charlie Baker’s budget office, comes after the state collected nearly 21 percent more in tax revenue than it did a year ago, an extraordinary jump.

Under the Baker administration’s accounting, much of the extra revenue would pay an estimated $3 billion refund due back to taxpayers should the state, as expected, trigger a 1980s-era law intended to limit state tax revenue growth to the growth of total wages and salaries.

After covering that credit, the Baker administration said, the state would have $1.9 billion in surplus revenue — itself a whopping figure.

Baker’s release of the surplus estimate served another purpose, too: It helped fortify his argument that the state has enough of a financial cushion to absorb the cost of both the surprise tax credit and a sweeping $1 billion tax relief package that, until last week, appeared on a glide path to his desk.

“The surplus is a little bit larger than we initially anticipated, even a couple weeks ago,” said Doug Howgate, executive vice president of the Massachusetts Taxpayers Foundation, a business-backed budget watchdog that, as recently as last week, estimated the surplus could reach nearly $4.7 billion. “It’s the highest I’ve ever seen.”

The Legislature had originally dedicated at least part of the surplus to helping cover a mammoth $4 billion economic development bill that included plans for $250 rebates to potentially millions of residents and more than $500 million in permanent tax relief, including expanded tax breaks for seniors, low-income workers, and others.

But the bill’s prospects faltered in the final chaotic days of the legislative session — which ended Monday morning — after Baker announced the likelihood of the state triggering the 1986 tax cap law known as Section 62F. The news surprised legislators; House Speaker Ronald Mariano even accused Baker of keeping them in the dark about its likelihood for months, a charge that Baker aides denied. And negotiations over the package ultimately fell apart amid doubts in the House that the state could still afford the tax relief plans.

Thursday’s release of the estimated budget surplus appeared to do little to assuage those fears.

In a statement, Mariano emphasized that with the $3 billion tax bill looming, the state still must navigate rising inflation and a likely economic downturn. “It’s absolutely critical that any additional relief does not deplete the Commonwealth’s financial resources,” the Quincy Democrat said.

State Representative Aaron Michlewitz, the House budget chairman, also preached caution, noting that while the surplus is dramatic, it’s largely in line with what lawmakers were expecting.

“The close to $3 billion that will take effect from 62F certainly changes how we should be spending the rest of that money,” the North End Democrat said.

Similar to Baker, state Senate leaders are far more bullish on the state’s ability to pass, and pay for, long-term tax breaks.

Senate President Karen E. Spilka said the tax cap law’s credit, which would be distributed proportionally to a person’s income tax liability, shouldn’t stop the lawmakers’ plans for a more “progressive tax relief package” that would largely target low- and middle-income workers.

“The Senate is committed to working with our partners in the House and the Administration to finally deliver the tax relief that residents deserve, as soon as we can,” Spilka said in a statement.

The tax relief debate is far from the only place where Baker is putting his stamp after the end of the legislative session. He also spiked a provision within a nearly $5.2 billion borrowing bill that would put a five-year ban on the construction of new correctional facilities or the expansion of current ones across the state.

The proposal included a carve-out for “accommodating” a transfer of inmates because another facility is closed, but Baker administration officials had raised concerns about a moratorium potentially tying their hands.

The Ripples Group, a state-hired consulting firm, also concluded last month that MCI-Framingham, the state’s only women’s prison, needs to be replaced, and that the state should build a $40 million 150-bed medium security facility.

In a letter to lawmakers, Baker said state officials have no intention of building new correction facilities “now or in the foreseeable future,” nor do they believe they’ll need to expand the system’s capacity with the state’s inmate population at a 35-year low. State officials say they plan to shut down the maximum-security prison in Walpole over the next two years.

But Baker argued that the bill could limit the state’s ability to modify other facilities and “maximize operational efficiencies.”

Senator Jo Comerford, a Northampton Democrat who sponsored legislation to pause prison construction, called Baker’s decisions a “setback, not an end.” But despite having Democratic supermajorities in both chambers, Baker’s veto appears likely to stand.

Lawmakers didn’t pass the bill until July 26, and on Monday they completed their final formal session for the year, meaning they now cannot override Baker’s veto outside calling a special formal session, a rarity on Beacon Hill.

Advocates for the moratorium argue lawmakers should nevertheless pursue that option.

Baker’s veto is “not surprising, and it’s also not acceptable,” said Mallory Hanora, director of Families For Justice as Healing. “We are urging the Legislature to take action and respect the will of the people . . . and call a special session. The Legislature left too much business on the table that affects people’s day-to-day lives.”