By Joan Gralla

NEW YORK (Reuters) - New York state's long battle over a $135 billion budget took another turn on Wednesday when the Democratic governor implored the minority Republican Senate leader for help enacting the next emergency spending bill.

Governor David Paterson was responding to newspaper reports that two dissident Democrats may trigger a government shutdown by rejecting next week's temporary spending bill.

The governor was appealing to the Republicans for help because his own party, the Democrats, have a razor-thin majority in the state Senate.

"I'm not going to respond to any threats, any thug activity, I'm not going to respond to any kind of blackmail in that respect," Paterson said at a televised meeting with legislative leaders in Albany.

Struggling to close a $9.2 billion deficit, New York missed its April 1 budget deadline. Its government has had to rely on emergency spending bills to keep running.

A shutdown could interrupt an array of state services, from health to transportation.

Paterson, saying the state could not wait any longer to start slicing healthcare spending, included $775 million of reductions in the bill the legislature enacted on Monday, but this strategy has stirred up opposition.

One potential rebel, Senate Democratic Majority Leader Pedro Espada of the Bronx, helped lead last year's failed coup attempt when he entered into a brief alliance with the Republican Senate Minority leader, Dean Skelos, before reversing course.

Espada said: "I will not vote for an extender with any major budget cuts."

Senator Ruben Diaz of the Bronx confirmed by telephone that he decided not to vote for another emergency spending bill on Monday, independent of Espada's decision.

"Either we have a budget or we don't," he said. "I cannot continue with the agony of these cuts every week."

DON'T EVEN THINK ABOUT A SHUTDOWN

Democrats have not accepted all of Paterson's health or education cuts. As an incentive, he offered to include all of the Medicaid cuts Skelos sought in next week's spending bill.

"All I'm asking you to do is help me and not risk the quality of life in the state of New York going into uncharted territory -- even you couldn't divine what would happen if the government were to shut down," Paterson said.

Skelos, who declined at the leaders meeting to say whether he would back Paterson, later told Albany reporters that the governor for the first time this year could count on GOP votes -- provided his next emergency bill included the Republican cuts in human services, Medicaid, and mental health.

"If those cuts are part of the extender next week -- and we believe it will be in the hundreds of millions of dollars we are proposing -- then a number of us in the conference, including me, will be prepared to vote for it," Skelos said.

(Additional reporting by Elizabeth Flood Morrow in Albany)

(Reporting by Joan Gralla; Editing by Kenneth Barry)