The vapor-liquid coexistence densities for water near the critical point were determined using a polarizable ab initio based model and grand canonical Monte Carlo simulations combined with the histogram reweighting technique. The predictions of the model used, which is found to give good agreement with experimental data at ambient conditions, are far below the experimental critical temperature and density. The saturation pressure is also overestimated. The source of this discrepancy may be related to the high pressure that the model exhibits even for liquid water. Since there is no fitting to experimental data, it is possible to refine the potential in a systematic way. In particular, an improvement in the sampling of the ab initio calculation for the repulsive part of the intermolecular potential is suggested in order to obtain better agreement with experiment at high temperatures and pressures.