First off, it's the Mayans, not the Aztecs. Second, NASA would be a viable resource since the Mayan calendar was based on the movement of Earth throughout the galaxy and universe, whereas ours is based upon Earth's movements throughout our solar system. The debate isn't about how would NASA know, the debate is about the Earth crossing a plane in line with the direct center of the galaxy or universe (can't remember which), which is why NASA would be a reliable resource as to determine whether or not this event will actually take place on the specified date. In actuality, the event already happend a couple decades ago, but most still hold on to the 2012 date as their is so much folk-lore about it.
The date doesn't mark the end of the world, it marks the end (and beginning) of a time period. Just as the Earth makes a path around the sun every 365 days, it also makes a path around the center of the galaxy (I think this is how it works, it's been awhile since I've researched this) So for the Mayans, and everyone else I guess, Dec. 21 2012 marks the end of one cycle (or "orbit" if you want to think of it like that), much like Jan. 1 2010 will mark the end and beginning of a new Earth year. Same principal but on a much larger scale.