How important of a role did the ideas from ancient Greek civilizations play in the development of the American political process?

The American Constitution was heavily based on the idea of democracy and a perfect world where people would have free speech and rights. The idea of democracy was derived from the earliest form of democracy, (direct) Roman democracy. As many people know, the Romans adopted a lot of Greek culture and ideas from taking over Ancient Greece in the times of the Roman Empire. This is what I think is how the American political process was formed from the basic standards of Greek civilizations.