And did they recognize it would mark the end of the Republic?
Augustus was never declared an Emperor by the Senate, and he wanted it that way. The Roman people had a strong dislike of monarchy or rule by a single person. He was given the title of First Citizen: it conferred on him most of the powers of an Emperor but kept the illusion of a functioning republic in place. Historians were the first to call him an Emperor; he never used the term himself.