The pilot reported that he was conducting a cross country flight and departed the airport with slightly less than 36 gallons of fuel on board. About 1.5 hours into the flight, he noticed that the fuel tank quantities were dropping rapidly. The engine subsequently lost all power, and he set up for a ditching in the Gulf of Mexico. After ditching, the pilot and passenger were picked up by a U.S. Navy helicopter and transported to a local hospital for observation. The airplane eventually sank and was not recovered. The pilot also reported that the engine consumed about 5.5 to 6 gallons of fuel per hour and he suspected a breach of the fuel system prior to the loss of engine power. The airplane was configured with two wing tanks that gravity fed to a header tank; both tanks fed simultaneously utilizing an "On-Off" fuel selector in the cockpit.