It's not all politics. I think the GOP just has a different view of deserters than liberals do. Liberals are more apathetic about them and some even encourage it to a point.
But yeah, it's pretty clear that Obama royally screwed up here, at least on the PR end of it, and of course the GOP is going to jump on it. Just like the libs would in a comparable situation that benefits them. But one of the reasons this is having such an impact on the public at large is that there are some very legit gripes here. Kind of easy to sell this thing as a fairly major screw up.