No, the Bible doesn't say this at all.
Actually, December 21, 2012 comes from the Mayan calendar. But I have to wonder, if that's a prediction, then why didn't somebody predict the end of their race before that happened?
Nostradamus also predicted a date, something like 2050, but people only tend to look at the few predictions that he got correct (and even those are said to be vague), versus the many more that were wrong, and choose to believe he's correct with this one.
Jesus said that only the Father knows the date of the world's end.
Satan knows his time is short, but he doesn't know how short. But you've got to think, if we knew, then Satan would know also...but he doesn't. No doubt he's just as freaked out about the final date, and has confused people with such predictions in order to gain company in his own anxiety.
Oh, hey! I found an old post from one of my previous blogs (on Xanga) that you may find interesting.