Public health efforts to control the Covid-19 pandemic have relied on both traditional epidemiological datasets and a variety of novel datasets, including large-scale surveys on health behaviors and attitudes. In the context of widespread vaccination rollout in the first half of 2021 in the United States we consider estimates of vaccine uptake, willingness, and hesitancy provided by the US Census Bureau, Axios/Ipsos, and Facebook/CMU. Despite very large sample sizes (and miniscule confidence intervals) we note a perplexing and growing divergence among these estimates over time: whose numbers should we trust to guide critical public health decisions? After establishing that the problem cannot be explained through selection bias alone, we extend a recently proposed statistical framework to quantify the sources of error in Big Data Meng (2018) and provide new estimates, with more reliable uncertainty intervals, for vaccine willingness and hesitancy.