The theory of spinning is that each pedal stroke takes far less effort then if you're pushing "too large" of a gear. Therefore, your energy reserves should be able to produce a lot more "easy" pedal strokes then "hard" pedal strokes, enabling you to ride longer.

There are two keys to spinning successfully though:
1) You need a smooottthhh pedal stroke, and that takes some time and committed practice to develop. If you are over-emphasizing the down-stroke portion of your pedal stroke, it's going to be hard to develop a fast spin, let alone realize any of the benefits of spinning.

2) You have to learn what the "right" gear is for you. i.e., there's more to spinning then just selecting an easy gear and pedalling a super-fast cadence. And you don't want to be in a hard gear straining either. Everybody's different as to what will feel "right" to them.