And John Edwards' support to either candidate could send Clinton or Obama over the edge, delegate wise.

I don't understand how these word work and could you please help me figure it out?

wise is commonly added to words to give the same effect as if with respect to were placed before them. It creates an expression that serves as an adverb of manner, answering the question "How?" or "In what way?" I've also seen it added without a space in between: delegatewise.

... could send C or O over the edge [with respect to / considered from the viewpoint of] (the number of) delegates.

This mode of creating expressions is fairly productive in English (after the pattern of otherwise), but can be used to excess in the popular press. The effect can be ridiculous at times, as in the following.

Sam is quite ignorant bookwise.
Ellen is very old-fashioned clotheswise.
Mr. Oldster was at a disadvantage agewise.

I understand! Thanks, CJ.