Bloomberg carries the day. Here from the NY Times:

After a spirited, emotional and at times raucous debate, the New
York City Council voted, 29 to 22, on Thursday afternoon to extend term
limits, allowing Mayor Michael R. Bloomberg
to seek re-election next year and undoing the result of two voter
referendums that had imposed a limit of two four-year terms.

The vote was a major victory for Mayor Bloomberg — a billionaire and
lifelong Democrat who was elected mayor as a Republican in 2001, won
re-election in 2005, became an independent last year, and decided just
weeks ago that he wished to seek a third term for himself in 2009 — and
for the Council’s speaker, Christine C. Quinn.
But the intense acrimony surrounding the decision left a sharply
divided Council and could ultimately damage the mayor’s popularity.

The new law, which earlier on Thursday sailed through a committee vote,
limits elected officials to three consecutive terms and applies to all
of the city’s elected officials. It has already begun to upend
municipal politics, reshaping the dynamics of next year’s races.