No time was ever specified in any of the ancient civilizations that predicted this phenomenon. Any predictions such as 11:11 UTC make no sense, first off the Mayans were in CST not UTC, and second the calendar ends on 12/20/12, it doesn't have half of 12/21/12 there and then stops mid day.
Realistically, the world could end at 23:59:59 UTC and still fulfill the 'prophecy'.