ALBANY — As New York’s deficits spiral toward historic depths, the state is starting to see its first increases in Medicaid cases in years.

State budget office figures project a 5-percent gain in cases under the government health care program for the poor in the 2009-10 fiscal year starting April 1. That would be 176,973 more cases, increasing the state’s share of Medicaid funding by almost $2 billion next year. That would also be a quicker uptick in Medicaid cases than is common for economic downturns.

The latest data on some of the New Yorkers being hit hardest by the state’s fiscal crisis comes as hope was resurrected for a millionaire’s tax.

“I can only tell you, among my friends, I’ve never heard one person say ’I’m going to move out of the city because of taxes,”’ said New York City Mayor Michael Bloomberg, the billionaire businessman. “Not one. Not in all the years I’ve lived here. You know, they can complain, ‘Oh got my tax bill, it’s heavy.’ But they’ve not ever thought that. My friends all want to live here and understand the value.”

While the mayor, sharing a Manhattan podium with Assembly Speaker Sheldon Silver, seemed to be voicing support for a millionaire’s tax, Bloomberg’s spokesman Stu Loeser said Bloomberg was talking about the overall tax burden.

“The mayor has always been opposed to New York implementing a millionaire’s tax because the people it would target are the very ones who are most likely and most able to assume an out-of-state residence, thus avoiding the tax,” Loeser said.

Bloomberg has a stake in easing $2 billion in cuts for the current fiscal year proposed by Gov. David Paterson on Wednesday. New York City’s lost state aid — after it already made deep cuts to fill its own deficits — includes a loss of $255 million in school aid alone.

If Bloomberg did support the millionaires tax, pushed in the Assembly, that could thaw opposition in the Senate’s Republican majority, which Bloomberg has supported for years.

Opponents say the tax, especially at a time of massive Wall Street layoffs, would drive the richest from New York with jobs in tow.

Paterson’s opposition to the tax increase wasn’t swayed.

“The governor has said repeatedly that new revenues won’t address the chief problem with the state’s finances — overspending,” said Paterson spokeswoman Risa Heller. “We need to spend less. Taxes don’t reduce spending.”

Mark Hansen, a spokesman for Senate Republicans, said Thursday that they are still opposed to raising taxes. The Republicans will lose their majority Jan. 1 under elections results of Nov. 4.

Paterson has proposed $2 billion in cuts, including midyear school aid cuts and tuition increases at public colleges, to fill a $2 billion deficit in the current budget and $12.5 billion he projects for the 2009-10 fiscal year.

But neither the Senate’s Republican majority nor the Assembly’s Democratic majority have yet committed to any cuts for the special session called for Tuesday.

“There’s going to be a process,” Silver said Thursday in Manhattan. “It’s actually started today. We have hearings taking place in Albany and we’ll continue tomorrow on the governor’s proposal. I hope to hear from our partners in government, like Mayor Bloomberg, examining some of alternative proposals to the governor’s and find some common ground with the Senate.”

Heller, Paterson’s spokeswoman, said it would be fiscally irresponsible to fail to act on Tuesday.