In this paper , we present moderately-high resolution ( \sim 65 \mathrm { km s ^ { -1 } } ) 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 ^ { 2 } 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 \dot { M } _ { \mathrm { tot } } ( H ) = 13 - 133 M _ { \sun } \mathrm { yr } ^ { -1 } for galaxies hosting a wind . These values of \dot { M } _ { \mathrm { tot } } , normalized to the corresponding global star formation rates inferred from infrared luminosities , are in the range \eta \equiv \dot { M } _ { \mathrm { tot } } / \mathrm { 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 ^ { \prime } -band magnitudes ) . We also attempt to estimate the average escape fraction \langle f _ { \mathrm { esc } } \rangle \equiv \sum \dot { M } _ { \mathrm { esc } } ^ { i } / \sum \dot { M% } _ { \mathrm { tot } } ^ { i } and “ ejection efficiency ” \langle \delta \rangle \equiv \sum \dot { M } _ { \mathrm { esc } } ^ { i } / \sum \mathrm { SFR } ^ { i } for our sample , which we find to be \sim 0.4 - 0.5 and \sim 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 .