Given the title of the book, it is not surprising that Kammen's main idea is that Americans are a people who are made up of paradoxes. Kammen argues that the way we are as people is a result of the tensions that these paradoxes have caused in our psyches.
Just to take one example of this, we Americans, Kammen says, have hugely idealistic visions of what we should be and what we should accomplish as a nation. Yet, at the same time, we are very suspicious of human nature and of the government. These are paradoxical attitudes to hold. Kammen argues that paradoxes like these end up making us frustrated and angry at ourselves and our society.
Kammen's main point, then, is that our culture, our society, and our attitudes come from a variety of paradoxical ideas that we believe.