ALBANY - Senate Republicans embroiled in a nasty budget fight with Gov. Andrew M. Cuomo are demanding that live-in partners like Cuomo’s girlfriend, food TV star Sandra Lee, submit annual ethics and finance disclosures as officials’ spouses already must do.

A Quinnipiac University poll released Thursday says 64 percent of New Yorkers agree. Even 60 percent of Democrats feel live-in partners of officials should publicly file data on the income, investments and business arrangements, said Quinnipiac pollster Maurice “Mickey” Carroll.

What began as a poke by the Senate early in the budget process has become a knife after Cuomo struck a deal for an ethics package with the Assembly’s Democratic majority, and never told Senate Republicans.

The deal requires legislators who are lawyers and other professionals licensed by the state to, in most cases, reveal their clients and exactly how they make big paychecks from private firms. The measure is aimed at exposing and preventing conflicts of interest. But Senate Republicans, many of them lawyers on the side, have staunchly opposed the idea as an infringement on their privacy and a violation of attorney-client protections.

Cuomo’s attorney, in explaining the Cuomo deal with Assembly Speaker Carl Heastie (D-Bronx), said the Senate bill to require disclosure by live-in partners isn’t even on the table.

“Actually, it doesn’t go to the source of the problem,” said Cuomo counsel Alphonso David. “And the ethics proposal that the governor advances actually goes to the source of the problem: Legislators that are engaged in outside activity where there is a conflict with their public work.”

Veteran good-government advocate Blair Horner of the New York Public Interest Research Group disagrees. He noted that New York City government and Cuomo, as attorney general in a legal settlement he wrote, have required domestic partners to provide income information.

“Government policy shouldn’t be guided by scandal,” Horner said. “Government policy should be determined by what makes sense. Situations are common now that weren’t common when these rules were written ... I think it’s legitimate to discuss.”

Skelos dug in Wednesday night.

“I was sort of surprised that the governor’s counsel announced that something was off the table,” Skelos said. “The conference will make that decision.”

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Then Skelos dismissed the importance of the Cuomo-Heastie deal, which can’t become law without the Senate’s agreement.

“They announced a two way (agreement) and you need a three-way in Albany to get something done,” he said.

The poll questioned 1,228 voters March 11-16 and has a margin of error of plus or minus 2.8 percentage points.