Well, author Steven Brill drops that bomb in his new book Class Warfare, published in August--though his source, former schools Chancellor Joel Klein, denied it in an 8/20/11 book review in the Wall Street Journal:
In addition, Mr. Brill quotes me saying that the reason we didn't get major reforms in the late-2006 teachers-union contract was because of the mayor's decision "to run for a third term." But so far as I know, the mayor didn't even contemplate running for a third term until 2008Picking up the news
As far as I can tell, Gotham Schools found the news first, in an 8/31/11 roundup article, without noticing the Klein review.
In a review essay headlined School ‘Reform’: A Failing Grade, in the 9/29/11 New York Review of Books, Diane Ravitch wrote:
Brill does have one piece of news. He writes that Bloomberg started planning to overturn mayoral term limits and run for a third term as early as 2006, not in 2009—as he publicly claimed at the time—in response to the economic crisis of 2008. Because Bloomberg secretly intended to run again, Brill claims, he tied Joel Klein’s hands in negotiating with the teachers’ union and dramatically expanded the city’s pension liabilities while getting insignificant concessions from the union in return.From the book
Here are two excerpts: