Playing around with Overthecap's calculator, honestly the cap situation isn't as dire as you'd think, assuming you can get your head around trading Rodgers and letting Adams walk. All would need post 6/1 designations but: 1.) trade Rodgers, 2.) Cut Cobb, 3.) Cut Kevin King, and 4.) Cut Billy Turner and that gets them $4mil under. That's not a terrible amount of blood letting IMO. Of course they need to be more under than that to rework the team and sign/extend who they need to, but they can get there with re-structuring Bakhtiari and Amos. Can save further by releasing one of the Smiths.
The point is, you can have Rodgers and Adams, or you can have a good NFL roster, but you can't have both.