The word "democracy" has apparently changed its meaning in the last few hundred years. A few sources (whose titles I can't recall) state that at the time of the founding of the US, "democracy" meant something more akin to "mob rule."
In other words, not something to embrace, but something to fear. Not a constitutionally-organized experiment in self-determination, but the French Revolution (something that many founders saw as a cautionary tale).
The deep mistrust in direct democracy is on full display in the Constitution itself. Only 1/3 of the Senate is ever up for election at one time. The framers were deeply worried about a "throw the bums out" revolt.
The Electoral College is another example. The framers didn't want a popularity contest that elected a lowbrow pandering to the the crowd's most base instincts. They wanted someone who could appeal to the elite members of the College and who shared their values.