The "aspirator motor", as it is called, is on the right side, around the passenger's air bag (outboard of the airbag, if I recall correctly). If you have small hands you may be able to reach around and find it. They often fail.
Did you do the tissue test as mentioned above?
As Stevebl says, do you have your temp wheel set at a reasonable temperature, e.g. 75 degrees? If so, and everything is working, yes, the system should definitely be able to eventually get cabin temp. down to the point where the blower will slow down. (At least mine does, even in 95 degree temps.)