People often use spatial metaphors (e.g., think "laterally," "outside the box") to describe exploration of the problem space during creative problem solving. In this paper, we probe the potential cognitive underpinnings of these spatial metaphors. Drawing on theories of situative cognition, semantic foraging theory, and environmental psychology, we formulate and test the hypothesis that larger physical spaces can facilitate divergent (but not convergent) processes in problem space exploration. Across two experiments, participants worked on a battery of problem solving tasks intended to represent divergent (alternative uses, shape invention) and convergent (remote associates, letter extrapolation) problem solving processes in either a large or a small room. In Experiment 1, participants in the larger room produced more novel alternative uses for everyday objects, and created more novel shape inventions, but generated less practical alternative uses, than participants in the smaller room. In Experiment 2, participants in the larger room (including a variant larger room) also produced more novel alternative uses for everyday objects, and less practical alternative uses, than participants in a small room, but did not create more novel shape inventions. These results suggest that spatial metaphors for problem space exploration may reflect meaningful cognitive phenomena: People may be able to search more broadly in a problem space if they are in an environment where broad physical search is a salient affordance; however, this effect appears to be relatively small and may depend on having sufficiently motivated participants.