I haven't seen anyone make that argument, and if I do, then I will most certainly jump on them. We are a representative democracy.
I don't think we disagree. Right now, we are living in a theocracy...a LIBERAL theocracy. We DO need more democratic involvement. We are cut off from our representatives, which is something the founding fathers were justifiably concerned with.
Specifically, they strenuously object to the constitutional amendment allowing individual citizens to elect Senators rather than government bureaucrats. They claim this has lead to the "downfall" of America and all the problems in the U.S. Senate can be blamed on voters choosing the Senators. They claim this is an example of "direct democracy" and mob rule (you can see examples on this very thread), when in fact the U.S. Senate is a representative body --- each Senator represents hundreds of thousands of people -- that is far removed from "directly" allowing citizens to pass any laws. They insist crooked government bureaucrats would appoint far superior Senators and that we can't trust ordinary citizens to make that decision.
They also strenuously object to other reforms allowing more democracy, like direct initiative and recall, claiming this is all part of an evil plot to "destroy the Republic", part of an evil scheme from 1913.
Personally I think those "conservatives" might want to spent a few months living in the "worker's paradise" of the Republic of Cuba, since they detest the idea of representative "democracy" so much.