The saturation mechanism for density and potential fluctuation spectra that evolve from linearly unstable electrostatic resistive interchange modes are investigated using particle simulations. Detailed comparisons of the nonlinear evolution, saturation levels, and resultant spectra between two‐ and three‐dimensional sheared magnetic field configurations are made. Significant differences appear. The single rational surface, quasilinear‐dominated evolution, fluctuation spectrum is adequately described using a density convection model. For the multiple rational surface case, the potential fluctuations are adequately represented by a balance between the nonlinearly modified source (curvature drive) and linear sink (parallel resistive field line diffusion). An accurate description of the density spectrum requires a mode coupling theory based on the two‐point density correlation evolution equation.