The baktun of 144,000 days, about 394 years, is the largest of the five places normally written, and thirteen baktuns from the Long Count origin fell on 13.0.0.0.0, which under the GMT correlation is 21 December 2012. A great deal was made of that date in popular writing, and almost none of it came from the Maya sources.
What the inscriptions show is that thirteen baktuns completed a previous era, since the origin itself is recorded as 13.0.0.0.0, 4 Ajaw 8 Kumku, and that the count did not stop there. Higher units above the baktun exist and are used: Classic inscriptions at Palenque and elsewhere give dates thousands of years in the future written with those higher places, which would be meaningless if the count were expected to end. One Palenque text reaches into the fifth millennium of the common era.
A very small number of Classic texts mention the 2012 period ending at all, and they treat it as a period ending. Maya organisations in Guatemala objected during the run-up to it that an apocalyptic reading had been attached to their calendar from outside, and the daykeepers who still run the 260-day count carried on running it through the date and afterwards.
The wider lesson is one this atlas has to apply repeatedly. A living or historical tradition acquires a modern overlay, the overlay circulates far more widely than the tradition, and the tradition is then read back through it. The 2012 literature is a large and recent example, and Jose Arguelles's Dreamspell, which borrows the Tzolk'in's structure under invented names, is another. In both cases the honest description separates what the sources say from what was later attached to them.