Flat Tire/Donut Issue
 

Had an issue with a flat tire on a 2004 Mazda 3 yesterday. Took off the tire and replace it with the donut in the trunk in order to move the car. Donut went on, but after tightening up lug nuts and lowering car, it would not move. donut was jammed against the caliper.
Is this a normal occurance? Any remedies? Will a full size wheel fit in the spare tire space?