There are no stop and id statutes, to my knowledge, that require you to physically show id. CA used to have one like that but it was struck down in Kolender V Lawson.
That might be what you're thinking about Rotor. No states require you to carry ID with you at all times, therefore it can't be unlawful not to provide it. In states that do have such statutes, what you described should work.
But some stop and id statutes go further than simply determining ID of a detainee. Some statutes call for an explanation of your activities. That's a 4th amendment nightmare IMO.
Regardless of where you are and what stop and id statutes there may be, ALL of these require that you be detained during a "Terry Stop". No officer can legally stop you, frisk you, and demand anything from you unless he or she can explain what crime you were potentially committing or about to commit.
I've done a lot of research on this, and it is surprisingly difficult to prove that something is legal (not showing / speaking your ID at request of an officer in NC).
But here is an interesting article tailored to NC, and written by a law firm that specializes in advising police departments across our state:
http://policehelp.net/pubs/2004/rollcallv3n7.pdf