Conflicts like this depend on an enoremous number of issues. This is true when there's two sides. When there's many individual nations engaging in an all out brawl, it's even more complicated.
A big question would be what alliances form. Obviously there's a desire to not ally with your enemy, but when your option is forming an alliance or getting blown away, alliances form.
All those complexities aside, I'd point out that California, Texas, and Virgina have more military bases than the other states. It's not a 1:1 mapping to success, but it certainly means they will have the resources to engage in a fight.
EDIT: SRM brings up an interesting point. Obviously how this predicament occurs will have a tremendous impact on the behavior of our armed forces. And, to StephenG's comment, this is the oath sworn to by the enlisted forces of the United States (emphasis mine):
I, (NAME), do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; and that I will obey the orders of the President of the United States and the orders of the officers appointed over me, according to regulations and the Uniform Code of Military Justice. So help me God.
It'd be a heck of a complicated situation to untangle!