Should America Defend Europe if it Won’t Defend Itself?

Iceland, in the midst of economic crisis, is considering closing its defense agency. Reports the Iceland Review:

Former Minister of Justice Björn Bjarnason described the Iceland Defense Agency as “remnants of times past” and said it might even complicate defense relationships with other nations. The Coast Guard should be focused on instead.

It may well be true that Iceland doesn't have many enemies. But if the Europeans don't believe they need defending, then isn't this another good reason to bring home America's troops? Certainly there's no reason for the U.S. to defend countries which don't bother to field militaries themselves!