Hmm, i'm not sure.
Does the wire work with the mac? The wire could be damaged, even if it looks fine. Check also if the xBox can connect to wireless.
I would try that first, see if there is a connection. Did you do manual setup in the airport configuration app? Check the settings to see if anything looks wrong.
Other than that, I am not sure. I have a Ps3 which hooked up fine (through wireless), I have not tried wired, as it is not in a good position to do so (id have to run it through the living room). If you're doing wired on Xbox live for connection quality, just try out wireless. People say they lag like crazy on wireless, but the air port extreme seems to handle it pretty well. I still lag sometimes on Call Of Duty 4, but that used to happen regardless.