The City Council speaker, Christine Quinn, and Mayor Bloomberg voiced opposite views on the term-limits debate yesterday, marking a detour in their close working relationship.

Mr. Bloomberg reiterated his support for the two-term limit for City Council members. “I think the public has spoken twice and they have spoken twice clearly. I don’t know that we can keep shopping for a different answer,” he said when asked about the possibility of a referendum addressing term limits. “The little you lose in experience, you more than make up in terms of fresh ideas.”

Ms. Quinn issued a one-sentence statement through her communications director, Sandra Mullin. “The speaker has long said she is interested in extending term limits and will work with members to explore possible options,” it read.

“This will be the first sort of public spat between the mayor and the new speaker,” a political science professor at Baruch College, Doug Muzzio, said.

Another Baruch political science professor, David Birdsell, said he saw yesterday’s disagreement as part of an ongoing difference between the two officials. “I wouldn’t see this as a major rupture between the mayor and the speaker. This is just a continuation of positions and needs that both have articulated in the past,” he said.

The issue was raised after the speaker’s office confirmed that Ms. Quinn commissioned a private poll that surveyed 600 New Yorkers about their opinions on term limits.

Ms. Quinn’s office did not release the results of the poll, but Mr. Muzzio said it may have included questions that would be used to frame the question of term limits strategically so that it could garner public support. The law could only be changed through referendum or legislation in the council.

Should the council pass legislation lifting the term limits, it is likely that the council would have to override a mayoral veto, a move that Mr. Muzzio predicted would lead to a lawsuit over the question of whether the council has the power to modify term limits through legislation.

In 1993, New Yorkers voted against a referendum to remove term limits, and in 1996 they voted against a referendum that asked about extending the limit to three from two terms. Members of the council will have to face the challenge of “how to reverse the impact of these two popular votes that give us the term limits that we have today,” Mr. Birdsell said.

Mr. Muzzio said there is no reason to believe that another referendum would bring different results, but that it might be “Quinn’s hope that if it went to referendum, the mayor wouldn’t be a vocal opponent.” He added that there would be “opposition to the proposal” to remove term limits but not to “the prospect” of considering revising the policy.

Ms. Quinn may be committed to breaking from her previous strategy of working with the mayor in order to follow through on promises that she made to other council members during the speaker’s race. As speaker, it might be better for her to break with the mayor than to “go back on your word to the people who got you there,” Mr. Muzzio said. He said he does not see the tensions causing any lasting damage.”I don’t think that the issue of term limits ought to sour the cooperative working relationship they have. … It’s not all huggy and kissy. All marriages have arguments,” he said.