The magnetic reconnection that occurs during the nonlinear development of the coalescence instability is considered. The structure of the reconnection region at the time of maximum current as a function of the resistivity eta is analyzed in detail using a compressible magnetohydrodynamic fluid code. It is shown that the numerical results concur remarkably well with a simple scaling analysis which predicts the dependence of the reconnection region structure on eta. It is argued that the flow topology is crucial in maintaining the ''fast'' reconnection rate. The results indicate a flux pileup solution in which the flux annihilation rate is approximately independent of eta, whereas the Ohmic dissipation rate scales as eta-1/3 . The possibility that these scalings break down at lower values of eta is discussed.