The reasons some Democrats support it are to punish Republicans by threatening their children with conscription and to break the military, both of which would supposedly discourage us from starting wars. (Well, that and their feeling of entitlement to do with others' lives as they wish.) Regardless of whether or not Obama secretly wishes this, he knows it's political suicide. Therefore he and the rest of the Dems, outside maybe those in very secure nut houses like Marin County or Vermont, will never reinstate the draft unless there is a war so large that Republicans would also support it.
I do wish he would go through with his promise to add a couple more divisions to the Army - those cuts Clinton made are devastating. But in a severe recession I suppose that's arguably not a smart thing to do.
I never much liked the idea of using the draft to make a point, but you clearly don't even understand the argument people who do support it are trying to make. It's not a way of punishing anyone (and how could it be, unless you're willing to stipulate that Republican kids volunteer for the military in much fewer numbers than Democratic kids). And it's not a way to "break" the military, a theory I have only ever heard in your post.
It's about trying to make sure everyone has some skin in the game. War is fun, war is badass, war is basically a Michael Bay movie in real life...as long as all you have to do to "support" it is slap a bumper sticker on your car. And this isn't a partisan issue, the military is a small enough percentage of the population that most people in both major parties can treat supporting the war (or not) as an abstract idea. The argument is that this wouldn't be the case when supporting a war meant your own children could become casualties in it. And I think that argument is probably right.
But it's still a stupid idea, because draftees DO hurt the military, which limits our ability to fight conflicts we might actually have to fight. And it might swing things too far the other way, with a majority failing to support ANY except the most dire of conflicts, because they don't want to be forced to fight at all.