The phase coexistence behavior of the solvent primitive model (SPM) is studied by constant pressure and temperature Gibbs ensemble Monte Carlo simulations. In the SPM, the ions are modeled with charged hard spheres, while the solvent molecules are represented by neutral hard spheres. Fluid-fluid phase separation into a salt poor and salt rich phase is found. At constant pressure, the critical temperature increases with respect to the critical temperature of the primitive model (PM) where no hard spheres are present. At constant temperature and for low pressures, the phase separation of the SPM transforms into the phase separation of the PM. For high pressures, it remains an open question whether there is an upper critical immiscibility pressure or whether a solid-fluid phase transition occurs first.