Cooperation is central to human societies. Yet relatively little is known about the cognitive underpinnings of cooperative decision-making. Does cooperation require deliberate self-restraint? Or is spontaneous prosociality reined in by calculating self-interest? Here we present a theory of why (and for whom) intuition favors cooperation: cooperation is typically advantageous in everyday life, leading to the formation of generalized cooperative intuitions. Deliberation, by contrast, adjusts behavior towards the optimum for a given situation. Thus, in one-shot anonymous interactions where selfishness is optimal, intuitive responses tend to be more cooperative than deliberative responses. We test this “Social Heuristics Hypothesis” by aggregating across every cooperation experiment using time pressure we conducted over a two-year period (15 studies and 6,910 decisions), as well as performing a novel time pressure experiment. Doing so demonstrates a positive average effect of time pressure on cooperation. We also find substantial variation in this effect, and show that this variation is partly explained by previous experience with one-shot lab experiments.