No one has any idea at this point.
There is no sense painting legs on a snake.
If Dunn is asking for something reasonable, it is the organizations fault for not making the deal. If he is asking for something unreasonable and doesn't get it when he tests free agency (because he is not willing to DH) again it will be the organizations fault for not stepping up.
Is it possible he gets some some crazy payday? Sure but that seems less likely.
All of the above involves less speculation than saying he won't be here next year. Granted Nats fans have been kicked around for long enough that I can understand the fatalism.