Using a spectral decomposition technique (Soto & Martin 2012, hereafter Paper I), we investigate the physical origin of the high-velocity emission line gas in a sample of 39 gas-rich, ultraluminous infrared galaxy (ULIRG) mergers. Regions with shock-like excitation were identified in two kinematically distinct regimes, characterized by broad ($\sigma >$ 150 \kms) and narrow linewidths. Here we investigate the physical origin of the high-velocity (broad) emission with shock-like line ratios. Considering the large amount of extinction in these galaxies, the blueshift of the broad emission suggests an origin on the near side of the galaxy and therefore an interpretation as a galactic outflow. The large spatial extent of the broad, shocked emission component is generally inconsistent with an origin in the narrow-line region of a AGN, so we conclude that energy and momentum supplied by the starburst drives these outflows. The new data are used to examine the fraction of the supernova energy radiated by shocks and the mass loss rate in the warm-ionized phase of the wind. We show that the shocks produced by galactic outflows can be recognized in moderately high-resolution, integrated spectra of these nearby, ultraluminous starbursts. The spectral fitting technique introduced in Paper I may therefore be used to improve the accuracy of the physical properties measured for high-redshift galaxies from their (observed frame) infrared spectra.