Is “I (you) don’t have to go any further than the mirror,” well-used phrase, or John Edwards’ invention?
Man in the mirror is a pretty well-accepted phrase, as well. (Even inspiring the Michael Jackson song of the same name. )
Looking in the mirror also has a biblical basis: “Anyone who listens to the word but does not do what it says is like a man who looks at his face in a mirror and, after looking at himself, goes away and immediately forgets what he looks like.” (James 1:23-24)
Looking in the mirror does imply introspection. Before criticizing or blaming others, you should first look in the mirror and realize that you have to take responsibility for your actions. I believe that is what John Edwards was saying.
Rather than an improvisation or a stereotype, the phrase is a variation of a "face in the mirror" trope. While some of the book links at the above ngrams link suggest intentions of introspection, reflection, and "looking deep within", other links merely use the phrase to refer to the person looking into the mirror. My understanding of John Edwards' remarks is that he is personally accepting responsibility. Accepting responsibility probably entailed some introspection but I think the phrase does not necessarily imply it.
The idea of looking in the mirror as a metaphor for realization about oneself is very common.
But there's no specific wording which is favored, there is no set phrase or idiom here for the idea. As long as something like 'mirror' and looking are involved, the intention comes across.