Don't know why the poor rating on the answer above, I agree completely. I would add a couple of other effects the war had on Americans at that time too.
First, this was the second major war Americans had fought in one decade, which meant another draft which means the younger brothers of those who had fought in World War II, and sometimes the same ones who had, would be leaving again to fight another war they may not come home from.
Second, Americans were unclear what we were fighting for. It ws an unpopular war, and Truman was an unpopular President because of it. Once the war ended in a cease fire, many Americans, and veterans for that matter, were angry that we hadn't "won" and what had all the blood and sacrifice been for if they weren't going to be allowed to win?
And it surely made them more afraid of communism and the Soviet Union, as stated above, and more likely to vote for hard core anti-communist politicians like Richard Nixon.
Of course, the Korean War's biggest impact was on the people who actually fought in it and their families. For them, it had a huge impact.
For most of the rest of the US, it did not make much of a lasting impression. It is sometimes called "the forgotten war."
Mainly, the war really cemented in people's minds the idea that the Cold War was for real. It convinced them that the communists would take any opportunity we gave them to try to expand.
I guess you could say that the war also helped to fuel McCarthyism in the early 1950s. McCarthy was able to use the sense of crisis at the time as a way to convince people that they needed to be afraid of communists within the US.