Res Publica versus Rule of the Demos. With regard to the former, if my history is not mistaken, what amounted to the Constitution of the Roman Republic was literally written in stone.
I had not really thought about this very obvious point, but America–as many have taken pains to point out in recent years–is by design a Constitutional Republic, not a mobocracy, which is how the framers of our Constitution viewed the Athenian Democracy.
Thus, Republicans in the name itself are truer to our Constitution than those who foster the rule of the Demos, the People, the mob.
Keep in mind that the word Demagogue has the same root, demos. Democracy and Demagogues go hand in hand.
And in reality, of course, the rule of the “people:” is almost always practically rule by an oligarchy which has simply duped enough people. Thus the “People’s Republic of China” is neither ruled by the People nor a Republic.