my impulse is that no adequately strong (probably any random 2200+ish but maybe any random IM+ is what's necessary. but hey, i'd personally doubt that an expert (2000+) would lose to a champion given a knight) player would ever lose to the world champion if given a knight, and probably 2 pawns would be enough as well.
As I mentioned above, this has already been tested (with a measly 4 game sample size ;-)) in the Kasparov-Chapman charity match a few years back. Chapman was a bit under 2200 and had two pawn odds in each game. Kasparov won 2.5-1.5.