Since your previous question had to do with Ancient Greece, I assume that you are asking about archaic Greece and have edited your question accordingly.
The first thing to note is that there were different types of government in various poleis (and at various times) in archaic Greece. The US government shares some characteristics with various of them. For example, the Spartans had what might be seen as a bicameral legislative system that is similar to that of the US. Of course, the Spartans also had kings, which is very different from our system today. The US was also like Athens in some ways. The Athenians were fairly democratic, with all male citizens being allowed to take some part in government. But the Athenians also sometimes had tyrants like Pisistratus, who ruled Athens for most of the period between 560 and 527 BC. This, too, is very different from our system today.
Modern US government, then, clearly shares some similarities and differences with various governments of Greek city-states in the Archaic Age.