Based on the severity of the situation and how he does his first couple of years i'd say 3-4 years.
Like Dom Capers obviously had a longer leash because he was working with an expansion team. And when he took them to 7-9 in their 3rd year and things were looking up, only for them to collapse back into 4-12 obviously he wasn't going to last much longer.
Nick Saban did have the Dolphins, 4-12 the year before, a game out of the playoffs the next year. If he goes 5-11 this year and 3-13 next year, with the talent we have, which is arguabley enough for a 500. season. He could be in trouble. If he goes 6-10 this year and then wins 7-8 next year he should be ok, but soon your going to want playoff wins, especially with an owner like Wayne Huizenga. I think Nick Saban is a good coach though, and he will turn this franchise around.