Animals can live anywhere. I don't mean that any animal can live anywhere, but every place is inhabited by something. Thus, the entire U.S. is still potential habitat for animals. There's also the argument that humans are animals, too.
Are you really asking how much natural habitat is left in the U.S.? That's an extremely tricky question to answer. First, how do you define 'natural'? There is perhaps no habitat in the U.S. - maybe even the world - that is completely unaffected by human activities. These effects, even if seemingly minor, may make the habitat unsuitable for certain species. The greater the change, the more native species disappear. It's a continuum. There's also the issue of scale; a habitat patch may be completely intact yet too small to support certain species.
Let me provide an example. Here in California, we have miles and miles of grassland that look, to the untrained eye, like natural habitat. However, they are composed mostly of exotic, invasive Eurasian grasses that replaced the native grasses, and many native wildlife species that used the native grasslands aren't there anymore. Is it still "livable space"? Certainly not for the species that are gone. At the same time, I could go to an industrial yard and find native birds there. Is it "non-livable space"? Try telling that to those birds! Some species are just more adaptable than others.