The points made by the pro-draft side about the alienation of the military from the public and the "out-of-sight, out-of-mind" conditions under which the professional force is laboring are worth considering, though. The best preventative of tyranny is a citizen army. (Sorry about the unintended irony, but that's life)
I think the Pentagon brass are caught between a rock and a hard place. Eternal war provides opportunity for career advancement, but the drain on the troops of multiple deployments has to be effecting the mission. While the brass probably don't care a whole lot about how much suffering is inflicted on the troops, there does come a point of diminishing returns.
If a draft were re-instituted, it would give the whole country a stake in the wars we are fighting, rather than being a messy unpleasantness only for those directly impacted and their loved ones. Insofar as the public can affect foreign policy (more unintended irony, alas), if more people had a stake in the war, then support would plummet fast. To which I can adduce Vietnam as evidence.
This doesn't help the troops in the short run, especially as it would take a lot of lead time for the public at large to get any measure of influence on the decision to go to war. Since Congress long ago cravenly abdicated the responsibility entrusted it in the Constitution, war is more of an administrative detail than a national choice. Instituting a draft would probably lower public support for the troops in the short run, which is all those poor buggers need. In the long run -- idealistically speaking -- a draft would hopefully make it less easy to fight wars requiring deployment of actual people, but it would do nothing for the remote-control drone war that Mr Obama is expanding. But drones are no final solution, because the ancient wisdom still applies: somebody has to walk in and squat on the territory, or there is no end to the war.
-- Mal