It is a bummer, but the good thing is that the Mac is under warranty and it won't cost you anything but some time. On a new machine, the cable was probably damaged during the assembly process and just took a bit of time to fail completely. As far as I know, these things are still assembled by humans, and when humans are involved, there's always the chance of an error.
You might want to call Apple about this, as I don't know if they would stock the cable at the store or not. You might be able to arrange for it to be there, or it might be better to send it off in the special box they send you. From what I hear, turnaround is really fast. I agree with letting Apple fix it rather than an authorized service center.
Good luck!