I think it may just have to play itself out, unfortunately.
You can try to tell her that every generation has been through something that terrified some people. Maybe tell her about the War of the Worlds broadcast, the Y2K thing (which at least had some semblance of logic in the sense that computers had not been programmed to go past 1999), the threat of nuclear war in the post-Sputnik years, the many conspiracy theories, etc. People used to think that the constellations were gods, that the sun orbited the earth, and the moon was made of green cheese. But we've grown beyond that.
Remind her also that she was afraid of X (monsters? night-time?) when she was little, but she outgrew it.
You're right, it doesn't help that adults are into this. It happened last year on Mamapedia too!
You might show her that she has a school calendar, everyone has a 2013 calendar, everyone's buying Christmas gifts, people are planning vacations and signing up for gymnastics and what not, the TV ads are promoting 12/25 and soon the 12/26 sales, New Year's Eve parties, and much much more.
It's a good time to talk about mob psychology (in her own terms) and not believing everything you hear. Also a good time to talk about those dumb tabloids at the check-out line that are full of nonsense ("baby born pregnant" or "Angelina Jolie is an alien" or whatever. Just because it's in print, doesn't mean it's true.
And let her know that others may be getting pleasure out of her panic, and it may be a form of bullying to prey on someone's fears like that.
And if the Mayans were so smart, how come they aren't around as a civilization anymore? They got a TON of things right, but not this one.
If she continues to get more and more agitated, get some short-term counseling just to help her anxiety.
Good luck. Let us know on 12/22 how she's doing.