How did goverment in Ancient Greece and Rome influence U.S. goverment today?

Answer 1

There was no such thing as "goverment in Ancient Greece". Throughout its history, the ancient Greece was not a single entity, but a collection of city states, some ruled by kings, others, by elected officials. What we call "the Greek democracy" today, should be called "democracy as practiced in Athens in 5th century BC".

Same goes for Rome. It started out as a republic, but eventually became an empire.

The greatest influences of Athens and Rome on the U.S. government, in my opinion, lie in their known shortcomings that the U.S. has attempted to remedy. For example, in Athens, elected officials (including judges) were not compensated at all or received token compensation. Therefore, only people of considerable means and people who expected to take bribes could run for office. The U.S.' response to the problem was to make federal judges the highest-paid goverment employees.

Rome's greatest problem (the one that led to the eventual demise of the Roman democracy) was poor civilian control over the armed forces. The U.S. used to have this taken care of, but in the post-9/11 madness, it seems to be slipping away...

Answer 2

Greece is considered the first democracy. Rome was considered the most influencial republic of the ancient world.