By Kenneth Lovett and Erin Einhorn

When Gov. Paterson takes to the airwaves Tuesday night, he’s going to say that the crumbling economy has ballooned next year’s state budget deficit to well over $6 billion, the Daily News has learned.

Two sources, one who reviewed a draft version of the speech and one who was briefed, said the deficit could be pegged as high as $6.4 billion, up from the previous $5 billion estimate.

“He’s going to put a real number on the problem facing the state,” one source said. “He’s basically going to say that we’re going to do what all New Yorkers are doing – cut our spending.”

Since suddenly taking office in March, the Harlem Democrat has repeatedly warned of the state’s declining economic picture and is convinced he needs massive cuts to reverse budgets built on borrowing and gimmicks.

While tonight’s five-minute address will be light on specifics, Paterson will call the Legislature into special session to deal with a looming home heating crisis and to cap local property taxes, a source said.

A draft version does not address reopening this year’s $121.6 billion budget, though the idea has not been ruled out, the source who reviewed it said.

Paterson will also call for increased federal help, the source briefed on the speech said.

“Because of the severity of the situation, that is why I want to talk to New Yorkers personally about the extent of what we see as financial problems,” Paterson said yesterday.

Paterson also took a shot at state lawmakers, saying his speech is intended to ensure that they understand the gravity of the state’s financial condition.

“People sitting in their homes know what the pain is,” he said. “I want to make sure Albany does.”

Assembly Speaker Sheldon Silver told The News he thinks Paterson is overstating the problem.

Silver wants to take a wait-and-see approach until October, when the second-quarter numbers are out.

“He’s being very cautious – overly cautious,” Silver said. “He doesn’t want a crisis on his hands.”

Meanwhile, a looming $2.3 billion city budget gap in 2010 could mean higher taxes and service cuts, city leaders warned.

“We all know there’s a train coming down the road and it’s headed straight toward us,” Mayor Bloomberg told the Financial Control Board, which monitors the city budget.

“We have to address these issues, no matter how difficult they are.”