Two-dimensional fully kinetic simulations are performed using global boundary conditions relevant to model the Magnetic Reconnection Experiment (MRX) (M. Yamada et al., Phys Plasmas 4, 1936 (1997)). The geometry is scaled in terms of the ion kinetic scales in the experiment, and a reconnection layer is created by reducing the toroidal current in the flux cores in a manner similar to the actual experiment. The ion-scale features in these kinetic simulations are in remarkable agreement with those observed in MRX, including the reconnection inflow rate and quadrupole field structure. In contrast, there are significant discrepancies in the simulated structure of the electron layer that remain unexplained. In particular, the measured thickness of the electron layers is 3:5 times thicker in MRX than in the kinetic simulations. The layer length is highly sensitive to downstream boundary conditions as well as the time over which the simulation is driven. However, for a fixed set of chosen boundary conditions, an extrapolation of the scaling with the ion to electron mass ratio implies that at realistic mass ratio both the length and width will be too small compared to the experiment. This discrepancy implies that the basic electron layer physics may differ significantly between MRX and the two-dimensional, collisionless simulations. The two leading possibilities to explain the discrepancy are weak Coulomb collisions and three-dimensional effects that are present in the experiment but not included in the simulation model.