Even in the case of Wisconsin, it looks like state residents can get a membership on a reasonably cheap yearly fee. Though I didn't see it mentioned, I'd assume this would include building access during normal hours. (Though perhaps that's a bad assumption?)

http://library.wisc.edu/visitors/borrow.html#wiscres

Informally, I checked the websites of a handful of state universities, and all had some way for residents to obtain borrowing privileges. It's far from a comprehensive survey, and I may be wrong in my assumption that borrowing privileges would allow normal building access. Still, at first glance it seems promising.