A model is developed to analyze the stabilization of the resistive wall mode (RWM) by plasma rotation. Central to the model is a cylindrical plasma that is ideal magnetohydrodynamic unstable in the absence of a wall, and possesses an internal resonance [J. M. Finn, Phys. Plasmas 2 , 198 (1995)]. This system is then a qualitative model for the actual toroidal external kink mode that is relevant in advanced tokamak scenarios. It has been shown in the past that the RWM can possess stability windows for modest rotation frequencies. However, the equilibrium parameter regime in which stabilization can take place is small. A nonlinear formulation of the problem is presented, with plasma rotation determined self-consistently by an equation of torque balance. It is found that, within the same small parameter regime, stability windows can be considerably extended at the expense of the growth of a magnetic island. On the other hand, depending on the initial rotation, the system can reduce the plasma rotation rate asymptotically to zero while the island continues to grow.