The force between two like-charged walls immersed in electrolyte solution is obtained for models that include solvent effects at the McMillan-Mayer (MM) level. In these models the solvent is not represented by discrete particles but exerts its influence through solvent-averaged ion-ion potentials of mean force which serve as effective potentials. This simplification allows the numerical solution of accurate anisotropic integral equation theories, and the anisotropic hypernetted-chain (AHNC) approximation is used in the present calculations. It is shown that the MM results may differ significantly from those of the primitive model (PM) which treats the solvent as a dielectric continuum. Most interestingly, we find that at the MM level the force between like-charged walls at small separations and with realistic surface charges can be attractive for monovalent counterions. This attraction is due to solvent effects on the effective counterion-counterion interaction and not to the correlated charge fluctuations that give rise to the attractions found for divalent counterions in the PM case. The possible relevance of our observations in the interpretation of experimental force measurements is briefly discussed.