ALBANY — New York State’s budget deficit, continuing its “bad news” ways, is projected as ballooning to $10 billion over the next 18 months. In addition, officials are warning that the state is likely to continue its traditional path of coming out of the recession later than the rest of the nation.

The projected combined deficit for fiscal years 2009-10 and 2010-11 stood at $6.7 billion in July, but has risen to $10 billion, largely due to a recessionary drop in collections of personal income and sales taxes.

The gloomier numbers came as Gov. David A. Paterson and legislative leaders, in a public meeting in Manhattan, failed Thursday to resolve the current deficit, which totals $3.2 billion.

“We’ve got to make those tough decisions,” Paterson implored the legislative leaders.

Democratic leaders, though, are resisting his calls for midyear cuts to public schools and to hospitals and nursing homes.

The state’s budgetary red ink is projected as swelling by an additional $6.8 billion in the 2010-11 fiscal year that begins April 1.

The number represents the size of the deficit if current spending and tax laws already on the books continue as is.

Paterson again rejected some legislative plans that critics long have condemned as one-shot gimmicks. Among those is a plan floated by Senate Democratic Conference Leader John L. Sampson of Brooklyn to raise $500 million by refinancing more than $3.2 billion in tobacco industry bonds held by New York following settlement of a lawsuit more than a decade ago.

Senate Democrats said the money raised could prevent any cuts to education.

“I will not shoot down your tobacco bond proposals again because they’re already dead,” Paterson told Sampson in the meeting. Last week, he said the bond refinancing plan’s revenues were vastly overstated.

By the end of Thursday’s meeting, the sides agreed — sort of — on some of the easier gap-closing ideas, such as raids on off-budget accounts to raise money for the general fund. Paterson is threatening to call the Legislature back into session in two weeks, and he warned after Thursday’s meeting that lawmakers would stay in town “until we’re done” closing the deficit.