ALBANY - One of the most far-reaching elements of the late state budget passed Sunday will give Gov. Andrew M. Cuomo unprecedented power to cut the spending plan if the State Legislature fails to agree on how to address potential federal aid cuts.

Cuomo’s “federal funding response plan” replaces the constitution’s practice of calling back the Legislature in a special, public session to arrive at a consensus on what to cut and how much, giving the governor leverage in the process by providing him the final word if the Legislature fails to agree to a plan. Under the law, Cuomo’s budget director will specify the amount of federal cuts that have to be addressed.

The new law is limited to taking action in 2017 and 2018 if the Trump administration or the Republican Congress cuts Medicaid and other funds by $815 million or more. The change addresses a 1970s court decision that prohibited a governor from “impounding” state aid passed in a state budget, including school aid, during emergencies from Wall Street downturns to the recent recession.

“Legislatures are not always quick to come together,” Cuomo said, “and are never quick to cut money. . . . If we didn’t have a device like this, I believe it would be better to keep the budget open.”

In January, Cuomo proposed having the power to unilaterally cut state spending as a response to federal cuts. The Legislature forged an amendment that gives lawmakers 90 days to come up with their own plan in a “concurrent resolution” before Cuomo’s spending reductions automatically go into place.

E.J. McMahon of the fiscally conservative Empire Center think tank said the measure is overdue.

“What he proposed was far too broad and not justified,” McMahon said Monday. “What he did, though, I think can be a template for a permanent fiscal reform.”

“Right now the governor is left wringing his hands” in a fiscal crisis, McMahon said, “and you have a regionally divided Legislature that can’t get its act together to come back and the governor can’t mess around.”

The Senate’s Republican majority called Cuomo’s original proposal “an overreach,” But it said the compromise in the budget bill GOP lawmakers passed Sunday “will allow members of the Legislature and the constituents they represent to have a voice in the process.”

After the Senate and Assembly rejected his original proposal in March, Cuomo was able to bring the measure back by linking it to several of his policy and spending issues in the state budget’s revenue bill. That avoided a separate vote on the budget-cutting measure and forced the Legislature to accept Cuomo’s cost-cutting plan or vote down the whole budget bill, which was packed with many items the Senate and Assembly majorities wanted.

Some political scientists and a good-government advocate remain concerned about the precedent that has been set, even with the new role for the Legislature.

“Amending the budget through a concurrent resolution is a novel and legally suspect way of handling the problem,” said Richard Brodsky, senior fellow at New York University’s Wagner Graduate School of Public Service and former Democratic assemblyman from Westchester. “But so is giving unfettered power to the governor to rewrite the budget. Until the constitutional duties of the Legislature and governor are made clear, the state is asking for trouble.”

“Can this be done by statute?” asked Gerald Benjamin, distinguished professor of political science at SUNY New Paltz. He said the measure contrasts with the design of the constitution. “It’s not clear to me that they could do budget cuts by executive action and/or concurrent resolution as specified in statute, overcoming constitutional requirements.”

“Our form of democracy with checks and balances such as these were added intentionally to prevent use of absolute power,” said Dick Dadey of the Citizens Union good-government group. “The state’s budget delay gave the governor extraordinary leverage in what was ultimately decided in the enacted state budget.

“That the Legislature now has a role in determining which future possible budget cuts may need to made in response to federal cuts is a good thing, but the Legislature’s power has been lessened under the agreement.”