I suspect that the delay you see is in the time it takes their warehouse not only to package your goods, but to also privately deliver it through their network to the most optimal ship point. You also have to factor in whether the carrier they've chosen supports delivery on the days you expect the item to ship.
Amazon should really make the difference between processing and shipping clearer, and perhaps factor it into the delivery estimates when you purchase. I've also always wanted them to let you chose carriers if you pay for a certain delivery speed instead of picking one themselves. I always have to cross my fingers that I don't get USPS for that important item.