Addressing the most pressing issues of our time, from climate change to Covid-19, requires enacting effective public policies. What are the psychological barriers to broad public support for such policies? What do these barriers tell us about how the social mind works? Our work suggests that liberals and conservatives disagree about effective policy solutions mainly for disagreement’s sake. Ordinary liberals and conservatives support climate and Covid-19 policies when political leaders from their party support them more than the same policies proposed by political leaders from the opposing political party. Such arbitrary partisanship is multiply determined. In part, people expect their partisan peers to toe the party line and they follow these partisan norms. Ordinary partisans also dislike and distrust members of the opposing political party, which undermines support for proposals from opposing parties. Although daunting, an appreciation of psychological barriers suggests strategies to overcome them. For example, policies proposed by trusted experts and bipartisan coalitions prevent polarization. Learning about widespread bipartisan support from ordinary people increases people’s policy support. And highlighting people’s values regarding good citizenship reduces political polarization. These findings illustrate how psychological scientists can help solve daunting societal challenges.