Many institutions—including American federal bureaucracies and legislatures world-wide—are characterized by one set of actors who possess the right to determine which policies will be enacted and an opposing set of actors who possess the right to delay the enactment of those policies. However, this interaction is not well understood. We provide a model that shows that a modest procedural right to delay but not veto the enactment of policies affords considerable influence over the policy agenda, so long as policymaking is time-consuming and time is scarce. In an application to the US Senate, our model exhibits properties that are consistent with common empirical claims about partisanship, polarization, and gridlock. It also justifies the considerable variation in the amount of delay imposed on the passage of various bills and the historic reluctance of the Senate to adopt reforms that would expedite the tedious cloture process.