Many political institutions use decision-making procedures that create veto players--individuals or groups who lack direct decision making authority, but nevertheless have the power to block policy change. In this paper we analyze the effect of veto players when policies are developed endogenously by actors with divergent policy goals. We first analyze policymaking activity and show that if veto players are moderate then competing groups on both sides of the political spectrum will develop policies for consideration. As veto players become more extreme, the pattern of activity becomes asymmetric, and one side disengages from policy development. For highly extreme veto players, there is no policy development and gridlock results. We also analyze the utility of centrist actors and show that veto players can have several different effects. Moderate veto players dampen productive policy competition because of their resistance to change. But some effects of veto players are surprisingly positive. In particular, when the status quo benefits a veto player and there is a skilled policy developer who is highly motivated change it, the veto player forces the developer to develop a higher quality proposal, which can be beneficial for centrists as long as the veto player isn't too extreme.
We apply our model to explain changes in patterns of policy development in the U.S. Senate, and to analyze conditions under which centrist members of the Senate may choose to maintain the filibuster.

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