I personally don't think it would be at all difficult to sell a draft in the event of an important war started by someone big against a strategic interest of ours (a large-scale low-tech invasion of South Korea by North Korean and Chinese troops).
I was thinking that somewhere short of a real nightmare scenario, yet perceivably beyond just slowly running out of options in Iraq, there may be a sweet spot that could be leveraged. Uncovering an al-Qaeda/Iranian/Syrian plot to firebomb the Capitol in DC? Finding an ex-russian nuke of unknown provenance in a basement in Anacostia?
Giovanni