Great post.
I think that in the United States, there is the popular belief that the left-wing (Democrats/Liberals) and the right-wing (Republicans/Conservatives) are (always) against each other. This also puts ordinary people who are inclined to support either wing against each other.
That said, I believe people should think that it is Democrats and Republicans versus the people. Remember that a population that do not cooperate with each other are very easy to control by those in power (by means of the divide-and-conquer strategy).