Berachos 32a

Gemara: "ויחל משה את פני ה R' Elazar said: This teaches us that Moshe prayed until he got sick." (I'm going according to the text of the Bach 4.) This gemara ties in well with the Gemara on 12b, "Rava says: If there is a scholar who needs mercy from heaven, one has to pray for him until he one is sick over it." The explanation for this, I've heard, is that when one feels another's pain to such a strong degree that it physically affects him, he is, so to speak, putting himself in the same boat as the sick person. Thus, he is, in effect saying, "Hashem, look! My friends illness is causing me pain, and I don't deserve that - would you please heal him, so that I can get better?" Certainly this would apply in our gemara, where Moshe was praying for the existence of the entire Jewish nation.