From here:
Without food, you can last around 60 days if you are a healthy adult with at least 11kg of fat in your body. It all depends on how much body fat you had in the first place. No human being can survive if he loses more than 40% of his body mass.

If you had more fat to begin with, you might possibly survive longer, though not by much.
So, looks like about 2 months is the ceiling. Another factor not mentioned is activity level. Presumably one could live even longer with a severely reduced level of activity. Obviously someone who sits on the couch watching TV is going to use fewer Calories than someone who runs marathons.