The resistive magnetohydrodynamics (MHD) model describes the dynamics of charged fluids in the presence of electromagnetic fields. MHD models are used to describe important phenomena in the natural physical world and in technological applications. This model is strongly coupled, highly nonlinear, and characterized by physical mechnisms that span a wide-range of interacting time scales. Solutions of this system can include very fast component time-scales to slowly-varying dynamical time-scales that are long relative to the normal-modes of the model equations. For this reason fully-implicit time stepping is an attractive choice for simulating a wide range of physical phenomena exhibited by the resistive MHD model. However, for efficient and scalable solutions fully-implicit methods require an effective preconditioner. In this paper, we propose and explore the performance of several candidate approximate block preconditioners for this system. One of these preconditioners is based on an operator-split approximation. This method reduces the system into two 2x2 operators; a Navier-Stokes operator and a magnetics-velocity operator with a Lorentz force coupling. Using previously developed preconditioners for Navier-Stokes, and an initial Schur-complement approximation for the magnetics-velocity system, we show that the split preconditoner is scalable and competitive with other preconditioners, including a fully-coupled algebraic multigrid method.