I want to use a soundbite of a speech I heard on the radio. When does something become public domain?

I think it is in the realm of 50+ years. Can the project wait that long? :)

All of these documentaries coming out have clips and soundbites of public officials, are they fair game?

If you were to record them yourself, then yes. However, if you get them from somewhere whose material is copyrighted (CNN, FOX, etc.) then NO. All these documentary filmmakers have contacted whoever recorded them and gotten a release (sometimes free, sometimes you gotta pay).