grammar - "I am gonna have to" vs. "I have to"

What is the difference between "I am gonna have to" and "I have to"?
When would you use the first one?

update: I am specifically asking about situations like the one described here.

Answer

Strictly speaking, "I am gonna have to" means the request is conditional.

In the type of case you're talking about, the request is not actually conditional. It's used in conditional form as a way of making it more polite. The basic idea is that if you're merely going to have to do something, that isn't as direct as if you actually had to do it right now. Indirection and extraneous words are typical ways of making something polite.