Solving a reinforcement learning (RL) problem poses two competing challenges: fitting a potentially discontinuous value function, and generalizing well to new observations. In this paper, we analyze the learning dynamics of temporal difference algorithms to gain novel insight into the tension between these two objectives.We show theoretically that temporal difference learning encourages agents to fit non-smooth components of the value function early in training, and at the same time induces the second-order effect of discouraging generalization.We corroborate these findings in deep RL agents trained on a range of environments, finding that neural networks trained using temporal difference algorithms on dense reward tasks exhibit weaker generalization between states than randomly initialized networks and networks trained with policy gradient methods.Finally, we investigate how post-training policy distillation may avoid this pitfall, and show that this approach improves generalization to novel environments in the ProcGen suite and improves robustness to input perturbations.