I vote yes.
The draft is the only thing that caused public outcry over the Vietnam atrocities, as it caused families from the entire socio-economic spectrum to be involved. Right now, the only people enlisting are the poor. And when they come home in body bags, the vast majority of the people don't know about it, and when they do, it's easy to say 'well, (s)he voluntarily enlisted, (s)he knew the risk'.
The truth is though most people enlist to escape extreme poverty, because it's the best option the have. It's not a real free, well-considered choice.
When everyone across the social spectrum knows somebody that will be shipped off across the globe, people will start thinking twice about supporting a meaningless war. People will start to REALLY care about the consequences and the cost.
When we go to war, it should be as nation. Not an economic choice costing us the 'cheapest citizens', like it is now.