ALBANY — A poll shows more than 70% of New Yorkers in every region, in both parties, and in every demographic group support a cap on property tax increases that is already doomed in the Legislature.

The Siena Research Institute poll found 74%of New Yorkers support Governor Paterson’s proposed cap of 4% annual growth in local school and government taxes.

The Siena poll finds fewer than three in 10 believe a cap would hurt education, as teachers unions and lawmakers claim. And 67% said a tax cap is needed “to force school districts to budget and spend resources more carefully.”

“It is clear no matter what argument you throw at them, voters said they want a cap. It is clear and loud,” Steven Greenberg of the Siena poll said. “They are not buying the argument of opponents.”

But lawmakers in the Senate’s Republican majority and in the Assembly’s Democratic majority apparently are. In its latest lobbying effort, the politically powerful New York State United Teachers union is calling the tax cap “disastrous” and “arbitrary” in a radio campaign.

NYSUT argues a cap would take away the will of voters in annual budget votes, impose artificial limits on spending, and worsen an achievement gap between rich and poor schools. The union said the poll questions were simplistic.

Mr. Paterson met with many of the school and labor lobbyists yesterday and said he remains committed to a cap, which was endorsed by his tax relief commission.

Mr. Paterson said his cap wouldn’t end local voter control because so few voters cast ballots on school budgets. He said he would like to see the May votes moved to general elections, where far more voters participate, but school advocates oppose that.

About 70% of school funding goes to salaries and benefits.

Yesterday, Assembly Speaker Sheldon Silver, a Manhattan Democrat, said a broader approach is needed that provides greater tax relief to the neediest taxpayers under current programs. Mr. Silver also said there would have to be a guarantee that state aid would replace any lost local tax revenue.

The Senate Republican leader, Joseph Bruno, also hasn’t let Mr. Paterson’s tax cap bill be introduced in his chamber. But Mr. Bruno says it’s because the cap is too weak. Instead, he reintroduced a 2007 bill that would allow school districts to phase out school property taxes completely and have the revenue replaced by state aid. That proposal went nowhere last year and isn’t getting any traction now.

Mr. Bruno, when questioned by reporters, wouldn’t say where that state aid would come from as the state faces $20 billion in project deficits over the next few years.

The result is that no progress is being made to curb the nation’s highest property taxes, which are 79% above the national average. The session is scheduled to end June 23.