The courts have stated on several occasions that the police do not have duty to protect you. The result of those cases is the fact that each individual is responsible for his/her life and no one else. The most famous case is Warren v District of Columbia.

Gun Owners of America discusses the case here.

Here is a more in-depth article on Warren and other cases including a deeper discussion of self defense.

Here is a Cato Institute Policy Report on self defense.