In this paper, we present moderately high resolution (~65 km s^-1) spectroscopy, acquired with the Echellette Spectrograph and Imager 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 χ² minimization to fit one- to three-component profiles to the Na I D interstellar absorption doublet in each object. Assuming that gas blueshifted by more than 70 km s^-1 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 _tot(H) = 13-133 M yr^-1 for galaxies hosting a wind. These values of _tot, normalized to the corresponding global star formation rates inferred from infrared luminosities, are in the range η ≡ _tot/SFR = 0.1-0.7. This is on average a factor of only 10 less than η from recent measurements of nearby dwarfs, edge-on spirals, and lower luminosity infrared galaxies. Within our sample, we conclude that η 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 ≡ ∑ / ∑ and "ejection efficiency" δ ≡ ∑ / ∑ SFRⁱ 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 that is optically classified as a Seyfert 1, are discussed separately in an appendix.