A larger tire diameter will lower the rpm's for a given speed. The lower rpm's is where the gas is saved. If the tire is made narrower, there is less frontal area, i.e. less overall aerodynamic drag. This also saves gas, since you need less HP.
If the tire is heavier, or wider, it takes more HP to get to that speed, so you lose gas mileage there. Once at that speed, this is not so obvious.
In summary, yes, a larger (diameter) tire is like gearing the engine down a bit, similar to an overdrive, and saves gas at steady cruising only. It may use a bit more gas to get there though.
(Most of these points were already mentioned in the above posts)