Did the US ever identify itself as a "democracy"? Didn't we always add the label 'representative"?

http://www.freerepublic.com/focus/f-news/1351222/posts

"Democracy: Operates by direct majority vote of the people. When an issue is to be decided, the entire population votes on it; the majority wins and rules. A democracy is rule by majority feeling (what the Founding Fathers described as "mobocracy"). Example: in a democracy, if a majority of the people decides that murder is no longer a crime, murder will no longer be a crime.

"Republic: Where the general population elects representatives who then pass laws to govern the nation … a republic is rule by law. Our republic is a form of government where power is separated, [our Founding Fathers knew that people are basically weak, sinful and corruptible, (Jeremiah 17:9)], pitting men against each other, making it difficult to pass laws and make changes.

"(Webster's dictionary definition: a government in which supreme power resides in a body of citizens entitled to vote and is exercised by elected officers and representatives responsible to them and according to law.)"

And yes. I do realize that this is a freerepublic site, but presumably they don't ALWAYS get it wrong.