The interaction between two charged walls neutralized by grafted polyelectrolytes ana mobile counterions is studied using a simplified model system, in which the charged monomers of the polyelectrolyte are replaced by "grafted" ions that interact with the grafting wall via a one-dimensional potential. Using a mean-field approximation, the model is solved numerically, and some analytic results are obtained for large separations. The behavior of the mean-field solution is checked against Monte Carlo simulations of grafted polyelectrolyte chains and is found to agree qualitatively. In salt-free systems there is generally a long-range repulsion due to free counterions, and then a short-range bridging attraction if sufficient polyelectrolyte is present. The addition of salt screens the long-range repulsion and usually lowers the pressure. A bridging attraction can occur at short-range and is significant mainly when the effective surface charge of the wall plus grafted polyelectrolyte is small.