ALBANY — Deficit reduction talks stalled again Tuesday, with Gov. David A. Paterson threatening to consider “all options,” including possibly state worker furloughs, to keep the state from running out of money next month.

State lawmakers, however, insist the talks are closer than the governor is revealing, and that the governor is holding out for more reliance on spending cuts than some of the politically less painful options being pushed by legislators.

The sides have been stuck on whether to slash more than $1 billion in education and health care spending, as Paterson proposed. Senate Democrats oppose the midyear cuts to public schools.

But the Legislature’s most powerful Democrat said Tuesday he agreed with Paterson that some school districts can afford to take a hit in their state aid funding in the middle of the year.

“I think that schools can absorb some cuts,” said Assembly Speaker Sheldon Silver. He would not say how deeply he might be willing to reduce school aid to help trim the state’s $3.2 billion deficit, but said poorer school districts would need to be held harmless.

Lawmakers were also discussing solving only part of the budget problem now, leaving some of the more difficult issues until a later date.

“I see it as one deficit, one plan,” Paterson responded.

The budget gridlock comes as Paterson has quietly struck a deal with some unions that would give labor groups more say in projects involving local industrial development agencies, which are government bodies that provide various financial incentives to lure private companies to a region.

Unions have demanded guarantees of greater involvement in IDA-funded projects, which economic development officials say would guarantee higher costs and, as a result, fewer projects by price-sensitive businesses.

The Paterson deal calls for different project cost levels before union-backed provisions kick in. For instance, an IDA project by a nonprofit, such as a hospital expansion, would require prevailing wages and certain mandated wage levels backed by unions to kick in if the project is valued at more than $10 million.

For-profit projects would qualify if the amount of the bonds needed for the project is greater than $4.65 million for upstate projects. A second test says the wage requirements would kick in if the value of the tax abatements provided by the IDA to the for-profit entity exceeds $96,115 over the life of the deal.

“These are extraordinarily low thresholds. It would encompass virtually every for-profit that an IDA would finance,” said Brian McMahon, head of the New York State Economic Development Council, which represents IDAs.

If those various limits are exceeded, local “prevailing wage” rates must be paid to workers involved in the construction of the projects. That virtually guarantees unions the work. But the deal also says that entities getting the IDA breaks — from nursing homes to YMCAs to small offices — must pay their workers a certain level of wages.

In upstate, the requirement would be a minimum salary of $14.68 per hour for workers at the nonprofits or private firms getting the IDA financing. In New York City, it would be $19.20 per hour. That, critics say, will be impossible wage levels for many nonprofits.

“This is Christmas come early for the unions,” McMahon said.

Peter Kauffmann, a Paterson spokesman, said the governor is working on an IDA bill he says “will create jobs, stimulate the economy and allow long-stalled civic facility projects to move forward.” More than $1 billion in nonprofit projects have been put on hold the past couple years while the IDA talks stalled.

Union officials involved in the talks could not be reached to comment Tuesday night.

Another nonbudget issue waiting in the wings is a bill legalizing gay marriage. While it has passed the Assembly, the bill has not been taken up in the Senate.

Senators on Tuesday said they expect the bill to be quickly brought to the floor after lawmakers finalize a defict reduction bill, possibly later this week.