I think we need to be fair to the President.
He never said the White House was a finely tuned machine. If you watch that part of the “Pres” conference he was very precise and clearly thinking carefully and using all of his brain power to give an accurate statement.
He very specifically said the White House was operating like a finely tooned machine. Toon being slang for a comic animation.
I am not sure what toon he had in mind when he said this. It could have been South Park or Tom & Jerry or Toy Story or American Dad. However it was 100% certain he was comparing the White House to a cartoon.