An organization connected to Ronald Lauder, the businessman who bankrolled campaigns to limit the time elected officials can hold the same office, is springing back to life following reports that Mayor Bloomberg might try to change the law and run for a third term.

The group, New Yorkers for Term Limits, launched a Web site June 6 and began a signature-collecting campaign in support of upholding the term limit law. It also commissioned a poll, the results of which were released yesterday, that found 73% of voters support keeping term limits in place.

The number of New Yorkers who said they were in favor of term limits decreased, however, when the question was changed. Only 61% of voters said they supported keeping the law in place after being told that the law allows city officeholders to hold office for a maximum of two four-year terms.

Those voters also were told that critics say it has done little to improve government and unfairly restricts voters’ choices, while supporters say term limits open the process to new people and break the grip of career politicians.

The executive director of New Yorkers for Term Limits, Allen Roth, said the organization felt compelled to act after a news report indicated that Mr. Bloomberg conducted a poll to see if voters would be interested in abolishing term limits.

“We thought that it would be a good idea to let the politicians know where the people who voted this law into law … stood on the issue several years after it had gone into effect, because it’s clear that the politicians are at least thinking about it. They have been since day one,” Mr. Roth said.

Pulse Opinion Research was commissioned by New Yorkers for Term Limits to conduct the poll, which surveyed 600 city voters.