Policy organizations need someone who is an effective manager. An MBA should prepare you to understand how to run a smooth operation. The most effective operations understand that they must run the organization efficiently, since their budget is derived from donations. You should also market yourself to trade organizations in industries that you are familiar. It won't necessarily shrink, but there will be a lot of lateral movements.
Committees hire attorneys to serve as counsel.
Beyond the legal training, they are looking for someone that understands and follows policy, especially as it pertains to the particular committee. Mr. Bennett, I am a recent graduate with an MA in Political Science. Let me put it this way, I don't have many employers contacting me with a Theorist opening, but I have successfully assisted Theorists in the job search. We assist all levels and have been successful at all levels. Entry-level job seekers require more help because they haven't established personal networks and value our contacts.