Gov. Andrew M. Cuomo started his second term with a zeal to address broad societal problems like income inequality, faltering public schools and waning trust in the criminal justice system.

Taking advantage of the strong budget powers afforded to New York’s chief executive, the governor peppered his budget proposal with policy plans, hoping to gain leverage against reluctant legislators.

But as Mr. Cuomo and lawmakers reached a budget agreement on Sunday night, many of his most ambitious goals were nowhere to be found. Instead, the governor stood poised to claim victory for what has become one of his hallmarks: an on-time budget in a state where budgets have chronically been late.

For all his aspirations, as the budget deadline neared, the governor blinked. Though he did secure some changes to ethics and education laws, he abandoned a number of proposals, pushing them aside until after the spending plan is passed.

As a result, the budget, which still needs the formal approval of lawmakers, would be Mr. Cuomo’s fifth in a row passed by the April 1 deadline, a feat of punctuality that has won a place at the core of his political brand.

The budget talks also shed light on the changed atmosphere in Albany: Mr. Cuomo, while still popular with voters, saw his influence diminished since his first term, when he demonstrated a mastery of the machinery of state government and legislators tended to swallow their frustrations, rather than fight back.

“As time goes on, the first-term mandate fades, and the legislative leaders on the majority side stand a little stronger with each passing year,” said Senator Michael N. Gianaris, a Queens Democrat, who added this about the final budget: “It’s enough to keep government functioning, but most of the major issues of the day have been peeled off of it.”

In his first term, Mr. Cuomo cited his on-time budgets as proof that he had extinguished the unruliness in Albany’s soap opera of a government. He has taken great pride in his achievement: Two years ago, he gave out hockey pucks to celebrate the “hat trick” of three on-time budgets, and last year he produced commemorative baseballs to celebrate his “grand slam” of four on-time budgets.

“It certainly reflects a more disciplined budget process by the state,” said Marcia Van Wagner, an analyst at Moody’s Investors Service. Still, she said, the substance of the governor’s budget, such as limiting spending growth, is more important than the date of its approval.

This year, Mr. Cuomo was again determined to produce a punctual spending plan — at the expense of its contents, in the view of people who think he folded too quickly.

Elizabeth Lynam, vice president and director of state studies for the Citizens Budget Commission, a nonpartisan watchdog group, questioned whether too many important issues had been dropped from the budget in the rush to ensure it would be on time.

“It should be quality over timeliness,” Ms. Lynam said, “not timeliness as the end all and be all.”

To that end, the budget deal struck on Sunday was notable for what it excluded.

A number of criminal justice reforms, developed by Mr. Cuomo after unarmed men died at the hands of police officers in Ferguson, Mo., and on Staten Island, were dropped. So were plans to raise the age of criminal responsibility to 18, from 16, and to impose new sexual assault policies at colleges across the state.

Even a hallmark of Mr. Cuomo’s tenure as governor, fighting against burdensome property taxes, fizzled this time around: A tax credit he proposed was dumped from the budget, too.

Mr. Cuomo faced resistance from both sides of the aisle. The Republican-controlled State Senate doomed his plans to raise the minimum wage and to pass the Dream Act, which would allow tuition aid from the state for undocumented students, while the State Assembly, which Democrats control, blocked a tax credit for certain donations to schools and scholarship funds.

Supporters of the abandoned proposals were not pleased that their issues were considered expendable as Mr. Cuomo worked to strike a budget deal.

“One thing he has taught us over the years is that he’s a brilliant political strategist, and our hope was that he would use that to make sure that the Dream Act was in the budget, and it’s not,” said Javier H. Valdés, co-executive director of Make the Road New York, an immigrant advocacy group. “And he as the governor needs to take responsibility for that.”

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