The double-layer interaction between one wall neutralized by both grafted polyelectrolytes and mobile counterions and another wall neutralized only by mobile counterions can give rise to an attractive osmotic pressure. This has been previously observed in both experiments and Monte Carlo simulations. Here a simplified model of this system is studied, in which the polyelectrolyte is replaced by "grafted" ions which interact with the grafting wall via a one-dimensional potential. In a mean field approximation, the model can be solved numerically, and certain cases are analytically tractable. The accuracy of the mean field approximation is tested by Monte Carlo simulations. Regardless of the exact form of the grafting potential, the simplified model proves to have the same qualitative features as simulations of the more complicated system where the configurations of the polyelectrolyte chains are explicitly included. In particular, in the absence of salt the interaction is repulsive at long-range but can be strongly attractive at medium-range, depending on the proportion of grafted ions and the width of the grafting potential. The interaction is again repulsive at short-range. The most interesting result is that addition of sufficient salt always causes the interaction to become attractive at long-range, primarily due to the change in the ideal contribution to the pressure.