Here in NC, we're dealing with a potential 20% cut across the university system. More likely it'll be 10-15%, but that's still not good. We're talking about having to cut non-tt positions and increase loads for tenured faculty, so hiring is likely going to slow if not stop at the public unis.
I have an offer from UNC Chapel Hill. How worried should I be? I think the offer is solid but does this mean that I'll never get a raise?
No, it doesn't mean you'll never get a raise. But it means you probably won't for a couple of years. At my school, this is the third year we haven't had COL increases or any merit increases. I don't see this changing for a couple of years, and there'll be a backlog to get through before it's "your turn" later.
The solution: seek external funding and don't depend solely on your salary. That's what I'm doing.