When I had to do a similar performance, I turned a few tunes into one. I did Satriani - 'Midnight', 'Day at the Beach' & 'Bamboo' mixed up (I don't like to think of it as a medley, but I guess it was).

Don't know if you can do it in your circumstance. If you can do the tapped stuff you can cover the rhythm part as well so that might be cool. If not, hopefully the thought translates to say hendrix / zep / James Blunt ( :eek: ) or whatever.

The advantages for this are:

1) If you know lots of bits of songs, you could build something with what you have rather than learn new material.
2) If you arrange it yourself, they won't know if you screw it up a bit as long as you 'style it out'... (Keep playing!)
3) If you use pieces you already know, there's less stress in performing them.
4) You might be able to showcase more techniques by combining pieces.

If you have to play a known piece, maybe think about something like 'Midnight'. If you can't play it already, it's not too tricky... make sure you cheat with a hair band or something around the neck though...