ALBANY - The state's second-largest public-employee union Tuesday rejected a contract proposal that called for pay freezes and health care givebacks. The vote delivered a rebuke to the Cuomo administration but also set the stage for thousands of layoffs.

The Public Employees Federation, which represents 56,000 professional and technical white-collar workers, voted down a five-year offer its leaders accepted earlier this month, with 19,629 (54 percent) voting no and 16,906 (46 percent) voting yes. The proposed terms included pay freezes for the first three years, higher insurance premiums and furloughs.

Reaction from Gov. Andrew M. Cuomo's office was swift.

Less than three hours after the results were announced, the administration said it had begun the process of laying off up to 3,500 PEF members, with workers receiving notices they would be out of a job in 21 days.

The outcome surprised many because just six weeks earlier the state's largest union, the Civil Service Employees Association, accepted a similar offer. CSEA leaders said members weren't thrilled by the terms but realized the state's economic reality.

PEF leaders adopted a similar line in urging members to accept the terms, saying it was better than layoffs.

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But after the results were in, PEF president Kenneth Brynien said his members resented the notion of givebacks after Cuomo successfully fought for the end of a surcharge on high-earning New Yorkers that some call the "millionaires' tax," which is set to expire on Dec. 31. Brynien also said PEF members were asked to accept slightly larger health care givebacks than CSEA.

"The sacrifices were too great, and they said, 'Enough is enough,' " he said.

Brynien said the union would ask the governor and his negotiators to return to the bargaining table and to "resist laying off thousands of our members as he has threatened."

But before the close of the business day, Howard Glaser, Cuomo's director of state operations, sent a statement to the media saying the administration had begun the process of issuing about 3,500 layoff notices to PEF members.

The 21-day notices sent to employees would seem to give the governor and union leaders a narrow window to renegotiate. But it was not immediately clear if that would occur.

Cuomo issued a statement saying, "In this economic reality, rising state workforce costs are unsustainable," and urging PEF members to reconsider. Later, Glaser sent a separate statement blaming Brynien for the contract's defeat."We spent months working with PEF's leadership and reached an agreement," Glaser said. "We now find out that they do not truly represent their membership."