There are two cycles which might be the source of this pseudoscience nonsense.
The first is the precession of the equinoxes,
http://en.wikipedia.org/wiki/Precession_of_the_equinoxes
which is the slow movement of the equinoxes (and also, of course, the solstices) around the ecliptic over time. The ecliptic crosses the midplane of the Milky Way in two places, (of course, as they are both Great Circles). This cycle takes 25,765 years.
Now it just so happens that the location of the Winter Solstice on the ecliptic is currently very near the midplane of the Milky Way
as seen from Earth. It is certainly possible that this conjunction was foreseen by Mayan astronomers more than a thousand years ago; if so they were remarkably accurate. But they don't seem to mention this fact anywhere or describe it in detail in any records or legends. Incidentally the closest approach of the Solstice to the galactic plane seems to have occured already, back in 1999, with no effects whatsoever.
The other cycle is the sine-wave-like undulation of the Sun and the Solar System as it passes through the disk of the Milky Way. This is caused by the distribution of mass in the plane of the galaxy and takes roughly 66 million years for a full cycle, 33 million years for half a wavelength. The midplane of the Milky Way in this context is defined by
an equal distribution of mass above and below the plane. This midplane is of course entirely different from the midplane of the galaxy
as seen from Earth, as the best estimates put us about fifty light years from the midplane as defined by the mass distribution;
http://solar-center.stanford.edu/FAQ/Qsolsysspeed.html
so we are not anywhere special at this moment.
Nothing special will happen in 2012, as there is nothing special about that date astronomically.