I think he stays in Washington in a deal that gets done in late June a la Stamkos. I think Washington has gotten their cap situation just enough under control to get it done.
Ironically, unloading Johanssen to NJ is one of the big steps in doing that. That move seemed like a absolute robbery at the time for NJ and now it appears that may not be the case. NJ is a team that desperately needs Carlson and it is ironic if their Johanssen trade is one that helps Washington keep him. Johanssen is now a full blown concussion case, a guy that may never be the same (see Clowe, Ryan), and even if he returns the same, you can't count on him or invest in him as a long term piece after hes missed essentially an entire year with head injuries. You are just waiting on the next one.
If Carlson somehow does get free I think NJ could really factor. Despite this slide here at the end, there is alot of positive momentum in that program right now around speed and youth. They have an MVP type player, a stud teenage center and are ahead of schedule. Carlson grew up in NJ, attended high school at St Joseph of Metuchen approx 15 minutes from Prudential Center, played youth hockey at the Prudential Center. Whenever the Caps play in NJ there is a huge "John Carlson Fan Club" contingent at the game. And they need his services desperately. They were also reportedly the high bidders on Shattenkirk last year (bullet dodged) - which if true would indicate their desire to go buy a top defenseman.