You could also be torquing down the string lock on the bridge too tight. Alot of people really put the Hulk Hogans on those things but you don't need to. It pinches the string alot harder on the corner where it bends to enter the saddle. It just needs to be tight enough to hold it in. I broke alot more strings early on from doing just that!
EDIT!!!
oh shit, I just realized that you said you were breaking them at the nut! I was thinking of the bridge - sorry. In that case I would probably just be worried about a burr as was already stated.

I realize now that I had absolutely nothing to add to this post...sorry I am an idiot!!!

HAHAHA