Andrew Sullivan has been mulling over this question on and off for several days because the presumed target was a congresswoman and because Loughner made some odd, incoherent statements about government and currency.
I suppose you might say that this was a political assassination attempt in the same way that you could say John Lennon's murder was a musical assassination, Rebecca Schaeffer's death was a sitcom murder and Gianni Versace died in a fashion killing.
I'm being only slightly facetious to underscore the problem with applying the label "political assassination" too broadly. A murder committed by a presumably psychotic person who happens to be obsessed with a political figure is fundamentally different from a murder committed by a non-psychotic person motivated by politics. Calling it a political assassination may make it easier to apportion blame to others, but I'm not so sure that in doing so we would also do justice to the truth.
Certainly there are political murders committed by persons with serious, non-psychotic mental disorders. As a rule of thumb, I would draw a categorical line at frank psychosis. So when political thoughts are intertwined with delusions, especially when those thoughts are processed within the context of a thought disorder, I would say that those thoughts are better understood within the framework of psychosis than the framework of politics. This may explain why attempts to politically characterize Jared Loughner's statements have been so strained. On the other hand, characterizing his publicaly known statements and actions using clinical constructs that apply to psychotic states requires no heavy lifting for a person who is well-acquainted with the signs and symptoms of psychosis.
As I've said before, certain serious cautions apply to my observations. Any formal diagnosis of Jared Loughner must occur in a face-to-face evaluation. The news media, blogs, and twitter are not reliable filters of information. We are, as yet, far from knowing the entire story, and that's assuming we will ever know the whole story.