I don't think Presidents, any of them, including Obama "own" the deep state. Obama had more control than most because he was younger, very shrewd, served two terms, and for the most part was on their side.

But in some respects, they have become a four branch of government and a power unto themselves. They support Presidents who throw more money their way and delegate more power to them, they resist the others.

I think Democrats tend to have more aligned interests with the deep state, but have a Democrat come into office and suggest that he or she will dismantle the power of the "deep state" and watch how quick it turns on that person.