That's completely incorrect.. The US does employ democracy as their system of government. This is different than the FORM of government, which is a republic. In other words, you are both a republic and a democracy, they describe two different things.
In a democracy, you vote on the issues. In a representative government (like the one in the US), you vote for representatives who will vote on the issues for you. When the founding fathers were discussing the formation of the government, most of them understood the dangers of direct democracy and designed the system as a representative republic in an effort to avoid those very problems.
I guess ballot proposals would be the only large scale example of democracy that is employed here, and if you want the definition of clusterfuck, look at what Californians have done to their government with ballot proposals. lol democracy democracy lol