Having lived in NC it is not Duke based on fan allegiance in the state. Many North Carolinians despise Duke almost as much as we do. Why, because most students come from outside of NC, many from the NE and Midwest. The program that's revered in NC is UNC. Anybody who is any body in the state went to UNC.
Don't get me wrong, UNC fans are obnoxious. But Duke fans overlay their obnoxiousness with an irritating level of superiority and smugness. From my time in the state here's my observation on the big four.
UNC: the state university is loved by most if not all North Carolinians.
Duke: hated almost everywhere by everyone.
Wake: everybody loves the underdog
NCState: who are they? If you can't get into UNC, apply here.