How does the American political system reach compromise?

Note: this is asked in response to lefteh’s answer to prevent that question from getting off-topic.

“The United States is built on political discourse, debate, discussion, and…er…I’m out of synonyms.
The point is that people talk to each other and develop their opinions. People can come together with their very different outlooks on the same situation, and create a compromise that works for everybody. That’s the underlying concept that makes this country so great.”

So how does the US democratic system reach compromise? To me, it seems very “all-or-nothingy”, i.e. you have to agree with one of two parties (you can vote differently, I believe, but it’s hardly of any use), and when one wins the elections the other gets nothing at all. Do I get that right? How does the US electoral system achieve compromise in the differing opinions among Americans?