In the United States, a popular explanation for rising partisan animosity and declining faith in democracy is that Republicans and Democrats misperceive each other to hold extreme policy attitudes. However, other aspects of group-attitude perceptions are likely as important to democracy. In particular, partisans may underestimate the diversity of Democrats' and Republicans' attitudes to harmful effect. This paper uses surveys and pre-registered experiments with representative and convenience samples (N = 6,158) to assess how much Americans underestimate within-party attitude diversity and to what consequence. We find that American partisans underestimate — by more than a factor of two — the diversity of each party's attitudes, and these misperceptions drive partisan animosity and perceived out-party threat. Yet, contrary to existing research, we find little evidence that American partisans consistently overestimate how radical the ``average'' Republican or Democrat is. Instead, our results suggest that ``perceived polarization'' may largely be a measurement artifact.