This time, the Council’s speaker, Christine C. Quinn, is one of its most ardent supporters. And the Garden management is a vulnerable political target these days, given the Knicks’ abysmal season, back-to-back sexual harassment lawsuits, and an outcry over the Garden’s having billed the city’s police academy $100,000 to hold graduation services.

David I. Weprin, the chairman of the Council’s Finance Committee, said budget pressures on the state and the city could help the resolution gain support in Albany. The tax exemption costs the city about $11 million to $12 million annually.

“I think the climate has changed,” Mr. Weprin said. “I can’t speak for Mr. Silver, but I don’t see how the state is hurt by revoking the tax exemption, and I think there’ll be a lot of pressure from members from the city, especially with talks about budget cuts.”

The Garden, owners of the Knicks professional basketball team and the Rangers professional hockey team, won the exemption in 1982 after threatening to move out of the city to escape high tax, energy and labor costs.

Edward I. Koch, who was mayor at the time, said in a recent interview that he believed the exemptions would end after 10 years. Instead, the Legislature kept the breaks in place for as long as the Knicks and the Rangers continued to play their home games at the Garden. Council officials said they knew of no other deal that offered a full property tax exemption with no end date.

In what could be a preview of the fight in Albany, City Council members debated whether it was fair to single out Madison Square Garden when government subsidies have been granted to the Yankees and Mets for new baseball stadiums and for a new basketball arena that will bring the New Jersey Nets to Brooklyn. Among them, the three teams are receiving more than $1.4 billion in subsidies over the next 40 years, including $230 million in property tax abatements, according to the city’s Independent Budget Office.

“The city has a history of supporting its teams and making sure they can function profitably in the city of New York,” said the Council’s majority leader, Joel Rivera, who voted against the resolution.