I think you're right on with your first thought; use the ones God gave you! I don't suppose you can adjust to a finger pick that quickly, anyway.

Thumb picks are good, but I prefer to use my nails rather than picks on my fingers. This may not help you for tomorrow's gig, but if you learn to use alternate fingers fro your finger picking, the next time you break a nail you could press another finger into service!

I use a picking method based around a thumb and two fingers. Generally I use the index and fourth OR the index and middle finger. If I break the fourth I use the middle - if I break the middle, I use the fourth. When all my nnails are in tact (normally)- I use 'em all, but alternate between the fouth and middle depending upon the sound I am looking for (the fourth gives a sharper tone to the high strings). I also use the middle finger to strike the string forward (as opposed to picking) for a sharp, percussive crack from time-to-time; this creates some interesting accents. If I have a broken index finger nail, I use the middle in its place. All of this is easier than it sounds, and can be accomplished with just a little perseverance.

Of course if more than one is broken, I'm still f*cked - so then I just use what stubs are left and hope it's loud enough! Best of luck!