Seriously. Mercenaries. Our biggest problem is that America doesn't like seeing it's boys come home dead. Why don't we try to get away from this idea of a whole army of well trained, well equipped young Americans in favor of a large number of hired troops under our command?
We can afford to pay them. There are clearly a lot of people in the world who have nothing better to do than wander around with guns. Heck, we gave the guns to a lot of them. Perhaps some of the more militarized African countries could supply troops in exchange for large wads of money.
Trying to think outside the box, here.