What would a citizen during the principate period think about the Republic? Did this change during the dominate? From what I understand, Augustus did a good job of veiling the erosion of the Republic, but did imperial propaganda last after his death?
Views varied greatly throughout different regions of the empire. The east has a much longer and more engrained tradition of deifying their rulers. This idea took much longer to be engrained in the West and particularly Italy. One of the reasons Diocletian never particularly cared to stay long in the city of Rome was because they still adhered to the Principate model and didn't really accept him as a divinely ordained ruler.