Using both survey- and platform-based measures of support, we study how polarization manifests for 4,313 of President Donald Trump’s tweets since he was inaugurated in 2017. We find high levels of polarization in response to Trump’s tweets. However, after controlling for mean differences, we surprisingly find a high degree of agreement across partisan lines across both survey and platform-based measures. This suggests that Republicans and Democrats, while disagreeing on an absolute level, tend to agree on the relative quality of Trump’s tweets. We assess potential reasons for this, for example, by studying how support changes in response to tweets containing positive versus negative language. We also explore how Democrats and Republicans respond to tweets containing insults of individuals with particular socio-demographics, finding that Republican support decreases when Republicans, relative to Democrats, are insulted, and Democrats respond negatively to insults of women and members of the media.