There are several reasons:
1) Nuclear technology is extremely expensive to develop and maintain.
2) The United States has a great abundance of natural resources that are cheaper to harvest and exploit: coal, natural gas, oil, wind and hydro. And, compared to nuclear energy, all of these are more energy efficient (that is, they will output more power than it takes to harvest them).
3) There is an ever-present fear of a nuclear accident happening, such as Three Mile Island or Chernobyl, even though these are isolated incidents that will most likely never be able to occur again.
4) Constant battles between environmentalists, NIMBAs ("Not in My Back Yard"), and government agencies have not only discouraged the further development of building and operating nuclear power plants, but there is almost no infrastructure on how to deal with the nuclear waste properly.