  The intrinsic column density (NH) distribution of quasars is poorly known. At
the high obscuration end of the quasar population and for redshifts z<1, the
X-ray spectra can only be reliably characterized using broad-band measurements
which extend to energies above 10 keV. Using the hard X-ray observatory NuSTAR,
along with archival Chandra and XMM-Newton data, we study the broad-band X-ray
spectra of nine optically selected (from the SDSS), candidate Compton-thick (NH
> 1.5e24 cm^-2) type 2 quasars (CTQSO2s); five new NuSTAR observations are
reported herein, and four have been previously published. The candidate CTQSO2s
lie at z<0.5, have observed [OIII] luminosities in the range 8.4 < log
(L_[OIII]/L_solar) < 9.6, and show evidence for extreme, Compton-thick
absorption when indirect absorption diagnostics are considered. Amongst the
nine candidate CTQSO2s, five are detected by NuSTAR in the high energy (8-24
keV) band: two are weakly detected at the ~ 3 sigma confidence level and three
are strongly detected with sufficient counts for spectral modeling (>~ 90 net
source counts at 8-24 keV). For these NuSTAR-detected sources direct (i.e.,
X-ray spectral) constraints on the intrinsic AGN properties are feasible, and
we measure column densities ~2.5-1600 times higher and intrinsic (unabsorbed)
X-ray luminosities ~10-70 times higher than pre-NuSTAR constraints from Chandra
and XMM-Newton. Assuming the NuSTAR-detected type 2 quasars are representative
of other Compton-thick candidates, we make a correction to the NH distribution
for optically selected type 2 quasars as measured by Chandra and XMM-Newton for
39 objects. With this approach, we predict a Compton-thick fraction of f_CT =
36^{+14}_{-12} %, although higher fractions (up to 76%) are possible if
indirect absorption diagnostics are assumed to be reliable.
