An important Roman contribution to American government is the idea of a "republic" or the creation of a representative democracy. In the Roman Republic, representatives were elected by the people to govern on their behalf in the Senate, similar principles were used in structuring the American system of government.
Not limited to citizens initially to mortals to Greek mythology and reality (sorry if it doesn't make sense ;-;)
The establishment of intellectual societies in America aided the spread of Enlightenment ideas.