Douglas Adams putting words into the mouth of Arthur Dent (HHGTTG)
“All through my life I’ve had this strange unaccountable feeling that something was going on in the world, something big, even sinister, and no one would tell me what it was."
“No,” said the old man, "that’s just perfectly normal paranoia. Everyone in the Universe has that.”
So, first, Bigfoot is real, and now there’s a shadowy, vague conspiracy behind the president who “really” runs things. Right on schedule.
Any predictions for what’s next? Fluoride is evil? Antivaccination? We’re all living on the inside of a concave Earth? My money’s on 9/11 trutherism.
Shhhhhh. It’s the Stonecutters
He had five: warmongering, shredding civil liberties, promoting Islamic socialism, reforming health care, and reducing CO2 emissions – the five points of the Pentagram of Evil as foretold by Nostradamus. 
… or the truth about how a warmongering liberty-shredding Kenyan Muslim could rig the elections to make himself President!
But to get back to sane reality for a moment: as already inferred by several posters, as the head of the executive branch of government, the President is analogous to the chief executive of any other very large organization. Any large organization will have skunkworks projects and renegade groups, but to suggest that these secretly have greater executive authority than the President is ludicrous conspiracy theory. If that were true, a lunatic like Curtis Lemay would have started World War 3 many times over. The real power over the Presidency is the same as the real power over Congress and it isn’t some secret Illuminati cult, it’s right in your face in the most public and obvious way: the special interests and lobbyists who control them both.
Even just in official, constitutionally-granted powers, Congress has a lot more power than the President. The difference is that Congress is made up of hundreds of individuals, to just one President, and Congress does not have hundreds of times more power than the President. There is certainly at least one group of people with more power than the President, and there may well be others… But there is no single individual in the country with more power.
Or you could say that there are wealthy and powerful “conspirators” running the nation, but they’re doing it really really openly.
Do not discount the possibility that they have gotten exactly the results they wanted.
But, obviously, the thread is not about that.
To expand on Chronos’ post…
The President isn’t in charge. He never has been, although most Americans who didn’t pay attention in Civics class don’t realize it.
There’s “checks and balances” in this country. We have a president, because in some situations it’s better to have a single individual calling the shots. But Congress has more power than the president when it comes to passing laws and representing the people. And SCOTUS is there to make sure that everyone plays by the rules, aka the Constitution. And they all have ways of overriding the others if necessary. Ideally, no part is more powerful than the others.
This system also makes it much more difficult for outside people and organizations to subvert the government. Getting control of the President isn’t enough. You also have to get control of several hundred congressmen, who are unlimited in the number of times they can run for office, and control of the Supreme Court who are appointed for life and don’t have any fear of losing their jobs. You may think, “Well, we’ll get control of the Speaker of the House which will give us control of all the representatives,” but he has to run for re-election just like everyone else, and if the other party gets a majority he’s out of a job even if he does get re-elected.
The whole system is basically much too chaotic and shaky to subvert. Push any part of it too hard, and it will just fall over and be replaced by someone else. The presidency, being limited to only two terms, is the most precarious of all of them, which helps offset the large amount of power available in the position.