This is a take on the saying The buck stops here
The saying "the buck stops here" derives from the slang expression "pass the buck" which means passing the responsibility on to someone else. The latter expression is said to have originated with the game of poker, in which a marker or counter, frequently in frontier days a knife with a buckhorn handle, was used to indicate the person whose turn it was to deal. If the player did not wish to deal he could pass the responsibility by passing the "buck," as the counter came to be called, to the next player.*
President Truman had a sign with this saying on his desk in the White House. (see the link above for some interesting info).
Here, Obama is saying that the responsibility resides with him- in other words, he is responsible.