Any reasonable argument about democracy has to take public opinion as exogenous.
What I want to say is, that public opinion is never illegitimate in a democracy. There is no 'right conscience' or something like that. So you can't claim the gov't to be illegitimate, if they have the consent of the people, even when your analysis finds, that people affiliated with that gov't create that consent. Der Amerikaner ist die Orchidee unter den MenschenVolker Pispers