For the most part, the American populace could really be considered militarist-neutral. We've been through periods of exaggerated suspicion, exaggerated hero-worship, and the more common phase of benign (or malign, depending on the period) neglect. I would say we're currently in a hero worship phase, which tends to create all sorts of perception problems. This is, of course relatively independent of political leadership, which will exploit or ignore the military and civil-military relations depending on their particular agenda.

By the way, the norm for American civil/military relations has been a small force operating on the edges of American awareness (either remote Frontier postings or overseas stations like we see today). It's the hero worship phase that creates things like military discounts and the high poll ratings for respecting service members (IMO, anyhow). The rift is no larger than it's ever been...and may even be smaller than it has been at some points in our history. But as mentioned in the thread JMM links to, it's a two-way street.