  In this paper, we present moderately-high resolution (~65 km/s) spectroscopy,
acquired with ESI on Keck II, of 11 ultraluminous infrared galaxies at z < 0.3
from the IRAS 1 Jy sample. The targets were chosen as good candidates to host
galaxy-scale outflows, and most have infrared luminosities dominated by star
formation. We use a chi-squared minimization to fit one- to three-component
profiles to the NaI D interstellar absorption doublet in each object. Assuming
that gas blueshifted by more than 70 km/s relative to the systemic velocity of
the host is outflowing, we detect outflows in 73% of these objects. We adopt a
simple model of a mass-conserving free wind to infer mass outflow rates in the
range (dM/dt)_tot(H) = 13-133 M_sun/yr for galaxies hosting a wind. These
values of (dM/dt)_tot, normalized to the corresponding global star formation
rates inferred from infrared luminosities, are in the range eta = (dM/dt)_tot /
SFR = 0.1-0.7. This is on average a factor of only 10 less than eta from recent
measurements of nearby dwarfs, edge-on spirals, and lower-luminosity infrared
galaxies. Within our sample, we conclude that eta has no dependence on the mass
of the host (parameterized by host galaxy kinematics and absolute R- and
K'-band magnitudes). We also attempt to estimate the average escape fraction
<f_esc> = Sum(dM/dt_esc^i) / Sum(dM/dt_tot^i) and ``ejection efficiency''
<delta> = Sum(dM/dt_esc^i) / Sum(SFR^i) for our sample, which we find to be
\~0.4-0.5 and ~0.1, respectively. The complex absorption-line properties of Mrk
231, an ultraluminous infrared galaxy which is optically classified as a
Seyfert 1, are discussed separately in an appendix.
