NEW YORK (CBSNewYork/AP) — Mayor Bill de Blasio promised Thursday to fight a proposal from Gov. Andrew Cuomo that would shift hundreds of millions of dollars in Medicaid and higher education costs from the state to the city.

As WCBS 880’s Peter Haskell reported, there’s no specific number as to how big the budget hole will be, but clearly it will be large.

“$500, $600, $700 million in the first year,” said Mayor Bill de Blasio said. “These are very big cuts that will affect the healthcare of the people of New York City, that will affect the ability of our young people to get an education.”

The mayor said the city will fight to have funding restored, but admitted this is a potentially debilitating situation.

“We will fight these cuts,” de Blasio said. “We will ask the assistance of both houses of the Legislature in fighting these cuts. They are unprecedented and they are unfair to this city.”

Cuomo and de Blasio have feuded repeatedly over a long list of issues, but de Blasio dismissed questions about whether Cuomo is using the budget to retaliate.

“I am going to keep being me. I’m going to keep doing what I believe in,” he said. “And I’m going to fight for what this city needs in Albany.”

Cuomo defended his proposal on Thursday, noting that his budget also proposes $20 billion to address homelessness, big investments in city schools, an overhaul at Penn Station and funding for the Metropolitan Transportation Authority.

He told WNYC radio the budget plan offered “the best arrangement for New York City for decades.”

“We’re bringing unprecedented state resources,” Cuomo continued. “They’re getting a lot of additional funding.”

Medicaid is the largest single component in the state budget. The federal government funds roughly half the Medicaid costs, the state pays about 35 percent, while the counties and New York City cover 15 percent. Currently, the state now limits the amount of Medicaid increases local communities must pay.

Cuomo’s budget would increase New York City’s responsibility for covering new Medicaid spending, saving state resources but costing the city an estimated $180 million next year and increasingly higher amounts in future years. De Blasio predicted the amount could exceed $1 billion by 2020.

As justification for the shift, the governor’s budget recommendation notes that New York City, with its five counties, is not subject to a property tax cap imposed on all other local governments in the state. This makes the city “uniquely positioned to assume responsibility for a portion of its Medicaid growth,” Cuomo said.

Lawmakers will soon begin work on the state budget, which they hope to pass before the start of the fiscal year on April 1.

(TM and © Copyright 2016 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2016 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)