The Poisson-Boltzmann theory for electrolytes near a charged surface is known to be invalid due to unaccounted physics associated with high ioh concentration regimes. To investigate this regime, fluids density functional theory (f-DFT) and molecular dynamics (MD) simulations were used to determine electric surface potential as a function of surface charge. Based on these detailed computations, for electrolytes with nonpolar solvent, the surface potential is shown to depend quadratically on the surface charge in the high charge limit. We demonstrate that modified Poisson-Boltzmann theories can model this limit if they are augmented with atomic packing densities provided by MD. However, when the solvent is a highly polar molecule, water in this case, an intermediate regime is identified in which a constant capacitance is realized. Simulation results demonstrate the mechanism underlying this regime, and for the salt water system studied here, it persists throughout the range of physically realistic surface charge densities so the potential's quadratic surface charge dependence is not obtained.