LAST week’s state Senate approval of Gov. Paterson’s proposed cap on school property taxes seems to have induced a nervous breakdown in the powerful statewide teachers’ union.

New York State United Teachers (NYSUT) has announced it will “suspend” its endorsement of 38 senators who voted for the cap, including all 31 members of the Senate’s embattled Republican majority. Looking to Tuesday’s special legislative session, NYSUT also fired a warning shot at Assembly members who even think of supporting Paterson’s cap, which the union claims “will harm children and public education.”

Senate GOP leader Dean Skeolos defied NYSUT to side with the Democratic governor after the union had dumped $350,000 into TV and radio ads claiming the cap would somehow lead to both higher taxes and “deep cuts to school programs.” The teachers’ allies in the union-backed Working Families Party and Alliance for Quality Education have chimed in with more anti-cap ads – a $1.5 million blitz raising the specter of “billions in education cuts, overcrowded classrooms, teachers fired.”

Paterson’s cap would hold the annual growth in school tax levies to 1.2 times the rate of inflation, or 4 percent, whichever is less. (And revenue generated by new construction wouldn’t count against the limit.)

The net effect would hardly be draconian. If it had been in effect over the past decade, the cap would have shaved about one percentage point a year off the average growth in total school tax levies.

So what’s all the fuss about? For one thing, the cap would make a much bigger difference during economic slowdowns, when property taxes tend to spike upward – as they did from 2001 to 2006, when school tax levies jumped an average 7.6 percent a year.

And the sudden prospect of any constraint on New York school spending – which goes mainly for teacher salaries and benefits – is a shocking state of affairs for NYSUT.

Since the mid-1990s, the union has been living in the best of all worlds. State aid has risen three times faster than inflation. The huge School Tax Relief (STAR) program initiated under then-Gov. George Pataki shifted more than $2.5 billion in homeowner property taxes to the statewide income tax base – and, in the process, shifted more revenue from New York City to suburbs and rural areas. School staffs have grown despite falling enrollment, teacher salaries have risen steadily – and New York tops the nation in per-pupil school spending.

The union has been able to dominate low-turnout school-budget votes across the state – sending $1 million in campaign funds this year to its local affiliates, as documented in a new report by New York Public Interest Research Group. But the cap would profoundly change the landscape of local school campaigns in two other ways.

First, while school-budget proposals would still require the approval of a simple majority of voters, it would take a super-majority of at least 55 percent to “override” the tax cap.

The cap law also lets local voters petition for referenda to “under-ride” the cap – in which case a simple majority would suffice to reduce the cap in any given year. (In this, the cap would represent the broadest expansion of direct democracy in New York’s history.)

NYSUT has a seemingly bottomless well of campaign funds and a potential army of thousands of campaign volunteers. But the union’s ability to swing contested legislative races remains open to question. Earlier this year, for example, the GOP candidate in a hotly contested Senate special election in northern New York was careful not to endorse a tax cap. Sure enough, he won NYSUT’s backing – but lost the race.

In 2007, a GOP political novice carried an upstate Assembly district heavily populated by government workers and represented by Democrats for 30 years. Strongly opposed by NYSUT, he made support for a property-tax cap the centerpiece of his winning campaign.

One of the union’s top leaders has said the cap would represent “the end of the public education as we know it.” Sadly, that’s a wild exaggeration. But Paterson’s proposal does represent an essential first step toward controlling New York’s excessive property taxes, once and for all.

And so, at this point, NYSUT’s worry is the taxpayers’ best hope for change.