Many people may argue that the two-party system doesn't work. However, having Democrat and Republican politicians helps to create a balance, so that, generally, no issue that is highly liberal or highly conservative passes. This balances things out, and extreme measures typically are less likely to pass than more moderate ones, and typically laws are not skewed toward one demographic.
A two party system may create arguments but that is what keeps us involved. With only one party, people are forced to believe in one thing. People will start to care less due to infrequent changes. Sooner or later the government will begin to fail and possibly lead to dictatorship or an anarchy of some sort.