Well, I would disagree... copyright doesn't only have to do with profit. The Fair Use Doctrine is fairly limited:
Fair use - Wikipedia, the free encyclopedia
One still has to ask permission to use a copyrighted work. The McCain campaign didn't (this is the second problem they had of this nature, btw). And, given Jackson Browne's history as a political activist, from No-Nukes, to Amnesty International to Vote for Change, and probably a myriad of others, he has a pretty good argument that not only did the use violate his copyright but also intentionally implied that he somehow endorsed the McCain campaign, something which, given the history, could be particularly egregious.
If you look at 17 USC 110, political use of copyrighted work is NOT one of the exempted uses.
U.S. Copyright Office - Copyright Law: Chapter 1
Now, it doesn't rise to the level of criminal violation of the copyright laws as what would occur in the case of piracy, but an argument for civil damages?
Well, counselor, tell me what you think --
U.S. Copyright Office - Copyright Law: Chapter 5
So in answer to your question, will he win? Dunno... depends on the republican judge who gets the case... But I sure as heck wish I were representing him.