That is not the problem. The problem is that we become INVESTED in a given party and vote for the party over the person.
It's actually a bit more complicated than that. We have a winner-take-all election system (and first-to-the-finish electoral college). There has been analysis which shows this tends to hit an stable equilibrium with two major parties. Once it becomes clear one of two parties is the only one with a viable chance of winning, people rationally don't pay attention to (or vote for) the minor party candidates.
There are many other voting systems which yield much better results. The problem is, they are much harder to explain and they don't "feel" as right. Americans are just never exposed to anything other than "you vote for one person, the creep who gets the most votes wins".
I'd love to see us try proportional representation, instant run offs, preference voting, or pretty much any other system. I just don't expect it to happen in any sort of scale in my lifetime. I certainly don't expect our elected officials to try changing it--they like the current system because they won using it.