P. D. Scott, in his book "Deep Politics and the Death of JFK" gives what I think is the canonical elucidation of deep politics or deep leadership.  He maintains that it is not in any sense a conspiracy.  It is simply that there are a number of people and organizations in our society that have large amounts of non-political power, but whose actions impinge on the political arena.  They end up reinforcing each other, not because there are any agreements (formal or informal) in place, but simply because their interests and actions are aligned.  Scott identifies the traditional military-industrial complex, other large corporations, the intelligence agencies and organized crime as major players.  To this I think today we can add right-wing religious movements - especially those with a Dominionist flavour.

It's not that they set out to create a "shadow government" - it's just that power works always for its own advantage, and those with money will always seek to pull the political levers.  The fact that all this lever-pulling has similar goals even though it comes from many different organizations is what gives the appearance of a layer of extra-political government.

Personally, I think Scott is being too charitable.  While his analysis might have been accurate in the early '60s, ever since the Chamber of Commerce memorandum by Lewis Powell in 1971 this accidental alignment has become much more organized and intentional.

It makes sense to me that because people with similar interests, degrees of wealth and world views will act in an aligned way, there is no need for a conscious conspiracy to exist for it to appear that there is. There appears to be a conspiracy when there is mainly a cohesion of values, interests, and goals among people of similar backgrounds and wealth. Since people in the 'deep leadership' stratum of society also have a lot of corporate, institutional and governmental clout, naturally their perspectives, values and interests are going to show up in the decisions made by the governing bodies of corporations, institutions and government. This overall picture doesn't preclude sub-sets of the 'deep leadership' having highly intentional programs for achieving what I'll call retrogressive (or authoritarian) ends. For example, Tom DeLay (more a demagogue than a 'deep leader') and his pals were highly intentional in their makeover of Congressional districting in Texas.
Add to that a little cronyism, and a little bit of overlap and connections between the groups, and you get a lot of back-channel communication that can help to synchronize their separate efforts. That doesn't require conspiracy; just communication that's not completely open.

Remember that it doesn't take a lot of people to make a really big mess of things. How many did it take to set the corporate culture at Enron? Or to destroy FEMA?