Those who say not a democracy aren't wrong. Neither are those who say it is. Sounds wishy-washy I know but it is really a matter of perspective. In the truest sense we are a republic. It's well understood by political scientists (and I have my bachelers in poli sci from Syracuse) that democracy in it's strictest form can't exist in a country much bigger than say, Switzerland. Nothing could be done fast enough to accomplish anything. Our republic, however, has democracy at its central core. The people directly elect their representatives in Congress and they directly elect their local governments. There is also the Electoral College when it comes to the Presidency that differs and the Judiciary which are appointed. Where it most significantly differs from a strict democracy is that these representatives are empowered to act as they themselves determine and they can and do act from time to time against what the majority of their voters wish at that moment. They have determined that they are acting for the greater good and with better knowledge of the subject. How this is still a measure of democracy is that if the people later feel that these representatives have not done the best thing they can be defeated in the next election and removed from office.
"Do not forget your dogs of war, your big guns, which are the most-to-be respected arguments of the rights of kings."
- Frederick the Great, King of Prussia