Only one problem. Julius Caesar invented Leap Year in about 45 BC to correct for the extra quarter day each year.
So if my math is right, we have had 514 Leap Years since is was invented. And the Mayan calendar dates to the fifth century BC--four hundred plus years before the invention of Leap Year. Which means that according to the Mayan calendar, it is sometime in July 2013 already. Doomsday came and went yet no apocalypse. Well, except for Obama being elected . . .