Not to pick nits, but the US of A was designed as a Republic, a Federal Republic, to make it harder for a government to overcome the will of the people (men with money or property who were entitled to vote at the time, not all men, certainly not indians (damn, into the red indian problem again) or slaves and certainly not women. Mostly age 21, and to be in congress 25, 30 for a senator, 35 for President and native born.
You can call it a democracy, if you want, but Lincoln said, "how many legs does a dog have if you call its tail a leg? Four, because a tail isn't a leg."
Franklin was asked what kind of government the constitutional convention had devised. He is reported to have said, "A Republic Sir, if you can keep it."
The national government is a lot stronger now than it was designed to be. This is probably true in most places, other than Somalia, where they don't have one.
Our government has evolved and gotten more democratic, but I doubt it has reached democracy, and except for some New England towns, democracy where all the citizens vote on the issues is likely not to work for large entities. Parliamentary systems are often representative democracies (although the old Soviet Union had a parliament.)
Democracy is one of those fuzz words that expands or contracts to mean what you want it to. The East Germans were the Democratic Republic of Germany. Well, if it means you have one party elections, what does "democratic" mean?