If Trump was referring to Truman, I don't know of any democrats that regard Truman as a favorite president.

Truman signed the National Security Act of 1947. This "reorganization" of the intelligence agencies is regarded in some circles as being the causative policy that created the Deep State. The Deep State is an assortment of silo committees that have exclusive decision power over major policy arenas, and the proceedings of these committees are outside the purview of the elected government. Essentially, a secret government evolved that manages the Military Industrial Complex, and whatever black projects they deem appropriate (i.e. Gary McKinnon's Non-Terrestrial Officers).