Nonlinear closure models of the two-dimensional magnetohydrodynamic equations predict that the turbulent diffusivity of magnetic fields in high magnetic Reynolds number flows will be strongly suppressed below the value predicted by simple kinematic models. The consequences of such "resistivity quenching" for models of dissipation and transport in astrophysical plasmas are profound. However, to date there has been little examination of the underlying assumption implicitly made by such models—that the quenching is associated with a reduction in the cross-phase between the velocity and the magnetic potential, rather than a suppression of the turbulence itself. In this Letter, we revisit the two-dimensional problem in an attempt to address this issue. The object of our scrutiny is the normalized cross-phase and its dependence on the initial magnetic field strength. This parameter is a useful diagnostic of turbulent transport and is insensitive to the decay of magnetic field. We present the results of numerical simulations that are consistent with the current picture of resistivity quenching as primarily a suppression of transport of magnetic potential rather than turbulence intensity.