  We study the capabilities of the MAJORANA DEMONSTRATOR, a neutrinoless
double-beta decay experiment currently under construction at the Sanford
Underground Laboratory, as a light WIMP detector. For a cross section near the
current experimental bound, the MAJORANA DEMONSTRATOR should collect hundreds
or even thousands of recoil events. This opens up the possibility of
simultaneously determining the physical properties of the dark matter and its
local velocity distribution, directly from the data. We analyze this
possibility and find that allowing the dark matter velocity distribution to
float considerably worsens the WIMP mass determination. This result is traced
to a previously unexplored degeneracy between the WIMP mass and the velocity
dispersion. We simulate spectra using both isothermal and Via Lactea II
velocity distributions and comment on the possible impact of streams. We
conclude that knowledge of the dark matter velocity distribution will greatly
facilitate the mass and cross section determination for a light WIMP.
