Let's take the common phrase "bite the bullet". If I want to trademark "bite the mullet", is there any barriers to that?
Being a common phrase is not a barrier to a trademark, in itself. For example “Bite the bullet” has been trademarked with the USPTO for restaurant services, for a target with cross-hairs and in several other classes at one time or another.
A less known or newly-coined phrase would have a very good chance of being available. I suggest a search of the TESS database.