Social media companies have come under increasing pressure to remove misinformation from their platforms, but partisan disagreements over what should be removed have stymied efforts to deal with misinformation in the United States. Current explanations for these disagreements center on the "fact gap"-differences in perceptions about what is misinformation. We argue that partisan differences could also be due to "party promotion"-a desire to leave misinformation online that promotes one's own party-or a "preference gap"-differences in internalized preferences about whether misinformation should be removed. Through an experiment where respondents are shown false headlines aligned with their own or the opposing party, we find some evidence of party promotion among Democrats and strong evidence of a preference gap between Democrats and Republicans. Even when Republicans agree that content is false, they are half as likely as Democrats to say that the content should be removed and more than twice as likely to consider removal as censorship.