What are you going to sing? Let's assume that you actually want to get through for your own nefarious purposes and you're not going in there to just tank it and get on TV for 30 seconds.
Are you going to retain your indie cred and wow them with something they've never heard? Are you going to sell out completely and do a medley of Take That hits to impress Gary? Or are you going to cynically pick a song that is so meaningful to you that you can't get to the end without blubbing like a newborn because your mum/grandad/hamster is sick/dead/fell down a well?
I might go with When You Were Young by the Killers. Easy to sing, everyone should recognise it, kind of at the indie rock end of the X Factor pop spectrum.