Mr. Cuomo succeeded in part by aggressively wielding a tool pioneered by his much-maligned predecessor, Gov. David A. Paterson: He threatened that if lawmakers missed the budget deadline, he would put his preferred cuts into an emergency spending measure, forcing them to vote for his budget or risk shutting down state government. That pressure helped drive lawmakers to the table in recent days, because refusing a deal with Mr. Cuomo would have meant giving up what scant restorations the Legislature had been able to wring from him.

Seeking to avoid the blistering attack ads from labor unions and hospitals that have pummeled past governors and weakened their hand with the Legislature, Mr. Cuomo also persuaded the state’s most powerful health care interests to draft a side deal with him that gave Mr. Cuomo the broad cuts he needed in exchange for concessions that would not directly affect the budget, like a “living wage” law for home care workers.

But Mr. Cuomo also made some concessions. He agreed to abandon a cap on “pain and suffering” damages for victims of medical malpractice, a controversial measure avidly sought by the hospital industry in exchange for its support of the health care cuts but strongly opposed by Assembly Democrats. A related proposal, to establish a state fund to pay for the future medical expenses of brain-damaged infants, survived the negotiations, drawing praise from hospital executives.

Advocates for increased school aid were livid over the deal, suggesting that Mr. Cuomo’s cuts — and his refusal to consider a “millionaires’ tax” to offset those cuts — would hurt students. “Governor Cuomo’s first budget makes heartlessly large cuts to our schools to finance tax cuts for millionaires and billionaires, and students in poor and middle-class districts will lose the most educationally,” Billy Easton, executive director of the Alliance for Quality Education, said.

The Assembly speaker, Sheldon Silver, a Manhattan Democrat, said he would fight to renew the income tax surcharge through a separate piece of legislation. “We still hope to convince our partners it’s the right thing to do,” Mr. Silver said.

The budget also did not include an extension of state rent regulations, which are set to expire in June, another issue that many Democratic lawmakers from New York City had supported.

Some details of the agreement remained unclear on Sunday. A district-by-district breakdown of school aid, with details that could trouble many rank-and-file lawmakers, would not be available until Monday, officials said. The deal also includes a cut of 3,700 prison beds but does not specify which prisons might close in the coming months.