While the President doesn't have direct control of gas prices, there is a lot of indirect influence by politicians. Under the guise of protecting the environment, offshore drilling and any exploration/drilling on federal lands has been regulated to a virtual halt. Supplies to refineries are thus artificially limited. It also gives OPEC the opportunity to set prices wherever it darned well pleases.
Then there is the matter of refining the oil. The limitations on refining, the regulations of geographical and seasonal blends, the almost impossible-to-navigate regulatory process to add refining capacity means that even a glut of oil will not solve the gasoline shortage.