Why didn't we draft men for the Iraq War owing to the lack of contribution from the French?

I, too, was deeply disappointed that France would not want to protect America from Saddam Hussein and decided not to go to war with us, but what I don't understand is this: without the contributions of the French, as well as the Russians, why didn't we make up for that deficit of manpower by bringing back the draft. Also, why didn't more eligible men, disgusted by the refusal, volunteer to fight in Iraq? I don't recall enlistment skyrocketing to make up for the French absence.