The 5 worst team in the NHL now are Pitts, Columbus, Washington, Chicago and Anaheim.
The first pick will be Ovechkin so who will have the first pick will take him.
Then I think you must look at what these teams need:
Pittsburgh need something in every position so they will go with the best prospect they could reach (Ovechkin, Malkin, Olesz if healthy, Barker)
Columbus: after Nash and Zherdev a good d-man like Barker would be a good choice.
Washington: Despite the struggling offense, they have Jagr, Lang, Bondra and many others scorers. Instead their defense is weak and Barker would be definitely a very good fit.
Chicago: again, their defense is pretty weak (despite Berard) but even the offense is not so good IMO. They are supposed to pick someone around the 4th so if Barker is available he would be their man.
Anaheim: need a d-man and a power forward. If possible they would pick Malkin or Barker.
So, at the end I think that Barker has a good chance to be picked 2nd, especially if Washington will have that pick.