Several recent theoretical studies showed that the spin-orbit interaction in narrow gap InGaAs/InAlAs double-barrier resonant tunneling structures might yield a highly spin-polarized current in the ballistic limit. In this paper, a nonequilibrium Green's function model is used to examine the effect of phase-breaking on the spin-dependent transport of carriers. The scattering is described as a local interaction with a bath of scatterers and treated in the self-consistent first Born approximation. Elastic and inelastic scatterers, with scattering strengths that cause a few millielectron volt broadening of quasibound states, have been found to significantly reduce the spin polarization. The magnitude of spin polarization has been found to be dominantly determined by the quasibound state broadening, while the interaction details are not significant.