I'll mention two things:
(1) NYC is a crazy quilt of ethnic and special interests - coalitions of constituencies win elections, not winning personalities.
(2) Bloomberg has ripped his mask off in his third term because there will be no fourth. And people are not happy about it and are letting him know.
Don’t forget the city council had to change their own term limit law to let him run a third time.
Its worse than ‘no pushback’. He seems to be a favored son.