It was one of the flash points of Mayor Michael R. Bloomberg’s bid to overturn term limits and clear the way for a third term: officials and workers with the Doe Fund, a nonprofit group that works with the city’s homeless, testifying at Mr. Bloomberg’s behest before the City Council in support of his effort. “There’s a reason Mayor Bloomberg is at 70 percent popularity,” George T. McDonald, the president of the Doe Fund, told the lawmakers, who ultimately voted to allow Mr. Bloomberg to seek another four years in office. “He acts in the best interests of the city of New York, and so should you.” Mr. McDonald was one of about 20 Doe Fund employees who testified that day in October 2008.