Prisoners' Dilemma (PD) experiments confirm and extend Axelrod's (The evolution of cooperation. Basic Books, New York, 1984) Shadow of the Future hypothesis: subjects cooperate in infinitely repeated PD, but they also cooperate until near the end in finitely repeated PD. So the extended hypothesis is that cooperation depends on the probability of continued play. Observational tests of this hypothesis, or even applications, have been rare at best. Here we not only apply but test it for interbranch cooperation under separated-powers constitutions, specifically those of the American states, using the end of governors' final terms as end points and the rate of overridden vetoes as the extreme case of a breakdown in interbranch cooperation. Controlling for a variety of factors, including divided government, we find support for the hypothesis, whose explanation of interbranch interaction fills a gap left open by Madison's Federalist 51: how republican government can control itself when what is needed is ''energy'' more than safeguards.