Simple thermodynamic arguments are evoked to show that the pressure dependence of the Flory interaction parameter of miscible polymer blends, as derived from small-angle neutron scattering experiments, is directly related to the volume changes on mixing for these systems. This approach is validated by comparison to available experimental data. We make contact with existing theoretical approaches and show that it is thermodynamically inconsistent to model a blend with nonzero chi as having no volume change on mixing. Since the entropic contributions that arise from these volume changes on mixing account for more than 50% of the pressure dependence of chi, the use of regular solution theory, where the pressure dependence is purely enthalpic in origin, gives an imperfect understanding of these situations. We finally show that, since the volume change on mixing is directly proportional to the chi parameter under ambient pressures, the critical temperature for any polymer blend will vary in an apparently "universal" fashion on pressurization This conclusion is in agreement with experimental data for a large number of polymer blends.