If you have AppleCare, I guess they are sending you a free replacement. I had to get my Mighty Mouse replaced because the scroll ball got gunked up beyond the usual cleaning method.
Guess I will have an interesting 5 - 10 business days until the new one arrives.
You can use just about any USB mouse, so you should just get a cheap one at the local computer store to have as a spare. Or you can use Mouse Keys, which is turned on in System Preferences +Universal Access+ pane
Mouse tab (use your keyboard numeric keypad in place of mouse).