We analyze the effects of veto players when the set of available policies isn’t exogenously fixed, but rather is determined by policy developers who work to craft new high-quality proposals. If veto players are moderate then there is active competition between policy developers on both sides of the political spectrum. However, more extreme veto players induce asymmetric activity, as one side disengages from policy development. With highly-extreme veto players, policy development ceases and gridlock results. We also analyze effects on centrists’ utility. Moderate veto players dampen productive policy development and extreme ones eliminate it entirely, either of which is bad for centrists. But some effects are surprisingly positive. In particular, somewhat-extreme veto players can induce policy developers who dislike the status quo to craft moderate, high-quality proposals. Our model accounts for changing patterns of policymaking in the U.S. Senate and predicts that if polarization continues centrists will become increasingly inclined to eliminate the filibuster.