It depends on the status of your Apple order. I tried the same thing and was unsuccessful. My order is in the "Preparing for Shipment" stage and cannot be canceled, even though it has not been shipped and will not arrive until October 5th. It's annoying because the local Verizon store has iPhone 5's in stock just waiting to be bought.
When you log into the Apple website and view your order status, if the Cancel option is there, you should be good to go.