The Cold War dominated American politics by forcing politicians to see practically every issue through the lens of that war.
Of course, the Cold War dominated American foreign policy. After all, this was, in the eyes of most American leaders, a struggle for the existence of democracy. Therefore, nothing was more important. This sort of thinking dominated US foreign policy from the time of the Marshall Plan, through the Berlin Crises, to the Vietnam War, and through Ronald Reagan’s relations with the Soviet Union. Everything that was done was done with an eye towards how it would affect the balance of power between communism and democracy.
We can also argue that the Cold War dominated American domestic policy. This, too, was because leaders needed to evaluate potential actions with regard to how they would affect the balance of power in the Cold War. This was true of the McCarthy Era. It was true to some degree of the ways in which leaders thought of civil rights. It was colored American thinking about domestic spending because it was necessary to ensure that the government spent enough on the military to continue to keep up in the Cold War.
Thus, we can at least argue that the Cold War dominated US politics for as long as it lasted.