The orthodox answer to the question posed in the title of this article is that the legitimacy of institutions has something to do with acquiescence to unwelcome public policy decisions. We investigate that conventional wisdom using an experiment embedded within a representative national sample in the United States. We test hypotheses concerning not only the effect of institutional legitimacy on acquiescence, but also the influence of partisanship, the rule of law, and simple instrumentalism on willingness to accept an objectionable policy decision. Our analyses reveal that legitimacy does matter for acquiescence, and that the Supreme Court is more effective at converting its legitimacy into acceptance than is Congress. Yet, many important puzzles emerge from the data (e.g., partisanship is not influential), so we conclude that Legitimacy Theory still requires much additional empirical inquiry.