There's an interesting EconTalk discussing the Ancient Greek economy where Russ Roberts asks his guest: "We certainly romanticize Greece as this great democracy; but it wasn't much like the United States, tell us about it"
But after Josiah Ober describes Athenian democracy it ends up sounding like what we call modern democracy is a very poor imitation.
http://www.econtalk.org/archives/2012/08/ober_on_the_anc.htm...
I think people are turned off by the idea of some random "crazy" running things, but that's exactly what I think would provide checks and balances to a government (namely, that the "crazies" don't reach a consensus as easily as the corrupt).
And on another level, our laws would have to be understandable! What would that be like? Would I actually know why I am being arrested?