The City Council will vote Thursday on Mayor Michael Bloomberg's proposal to change the term-limits law.
A spokesman for the council speaker said the last minute addition to the agenda was made Tuesday.
Typically, when the speaker puts a bill up for a vote, it means there is enough support to pass it.
Meantime, a new poll finds New Yorkers overwhelmingly believe the City Council should not have the power to extend term-limits for officeholders. That should be up to the public, respondents say.
The Quinnipiac survey of registered voters finds that, by a margin of 89 to 7 percent, they prefer a referendum over letting the council decide.
The 51-member council is considering a bill that Mayor Michael Bloomberg has been pushing. He wants another four years in office and is trying to change the law so that he can have a chance at a third term.
The poll, which has a margin of error of 3 percentage points, also finds that voters oppose giving elected officials the option of a third term. That margin is much closer, at 51 to 45 percent.