Decades of research in control theory have shown that simple controllers, when provided with timely feedback, can control complex systems. Pushing is an example of a complex mechanical system that is difficult to model accurately due to unknown system parameters such as coefficients of friction and pressure distributions. In this paper, we explore the data-complexity required for controlling, rather than modeling, such a system. Results show that a model-based control approach, where the dynamical model is learned from data, is capable of performing complex pushing trajectories with a minimal amount of training data (10 data points). The dynamics of pushing interactions are modeled using a Gaussian process (GP) and are leveraged within a model predictive control approach that linearizes the GP and imposes actuator and task constraints for a planar manipulation task.