Gov. Cuomo’s operations chief yesterday was quick to blast the leadership of the Public Employees Federation for “failing to effectively communicate the benefits” of a tentative contract deal that PEF members voted overwhelmingly to reject.

But if Cuomo wants to know the real reason why so many PEF members were willing to snub their noses at this deal, he might look toward the onetime engineering marvel that spans the churning confluence of the Harlem River, Bronx Kill and Hell Gate.

In July, Cuomo and PEF leaders reached a tentative five-year contract that offered a modified no-layoff pledge in exchange for some significant concessions, especially on the sharing of health-insurance costs. But thanks to a nearly 30-year-old state law known as the Triborough Amendment, the vast majority of PEF members knew they could avoid making any financial sacrifice simply by voting “no.”

Triborough, historically rooted in a contract dispute involving toll collectors at what is now known as the Robert F. Kennedy Bridge, ensures that provisions of a public-sector union contract remain in effect even after the contract expires. As local government officials have been pointing out for years, this puts management — meaning, ultimately, taxpayers — at a distinct disadvantage when trying to bargain for lower costs.

Cuomo had won PEF’s tentative agreement to a three-year freeze in base salary and five payless “furlough” days this year — essentially, a temporary pay cut. Union members would have to take off another four payless furlough days in 2012, for which they’d be reimbursed the next year.

They’d get 2 percent salary increases in years four and five, but they’d also pay for a larger share of their health premiums. As one union member told a labor publication last month, “We have the Triborough Amendment — why do this to yourself?”

Why, indeed? Yes, up to 3,500 PEF members will now be laid off. But more than 90 percent of the union membership will keep their jobs while avoiding payless furloughs and higher insurance premiums. What’s more, thanks to Triborough, many workers will also continue pocketing the annual longevity “step” increments mandated by the civil-service-salary schedule — just as they would have done if the squishy “freeze” in base salaries had been ratified.

Cuomo had reason to hope for a better outcome. After all, members of the state’s largest union, the Civil Service Employees Association, ratified an almost identical deal last month, thus making it unnecessary for him to lay off CSEA workers.

The different results probably reflect, in part, the distinctly differing circumstances of the two employees groups. CSEA represents the state’s lower-paid blue-collar and office-support workers — drivers, janitors, secretaries, mental-health attendants and the like, who tend to live closer to the economic margins. PEF bargains for the government’s better-paid professionals, including lawyers, tax auditors, parole officers and research scientists.

Because both contracts would increase health-insurance premiums on a sliding scale, with higher hikes for better-paid workers, PEF members as a group stood to pay more. Except … Triborough made that unnecessary.

Cuomo is now left with no choice but to commence layoffs, never an optimal solution — and one that will not, in any case, yield the same lasting health-insurance savings as the rejected contract.

The state’s county executives, mayors and school officials may be tempted to see poetic justice in the governor’s first significant labor setback. After all, the main reason the Triborough Amendment hasn’t been challenged in Albany — even though it tops most municipal and school-district mandate-relief agendas — is because Cuomo has been unwilling to go near it.

Perhaps now he’ll rethink his position.