This particular document doubles as both an NDA and a non-compete. I did some research, and it looks as if my particular state does allow for non-compete agreements to exist.
What happens if you refuse to sign it? Is it: "sign or be fired?". Also if you are in a financial position of strength, it may be advantageous and savvy to fight it by not signing. This way you may be able to get the terms modified to be less onerous. If they are presenting it like a contract of adhesion (sign it as-is or be fired). Then
you don't have much choice unless you can live without employment for a while or move to a state with more employee-friendly laws.
I'm not a lawyer, and I'm not suggesting that I am, but you may want to ask about the impact of not signing the non-compete as signing it will limit your future employment opportunities. You may also want to talk to a lawyer in your state. You obviously are concerned about signing this.