The COVID-19 outbreak has focused attention on the use of social distancing as the primary defence against community infection. Forcing social animals to maintain physical distance has presented significant challenges for health authorities and law enforcement. Anecdotal media reports suggest widespread dissatisfaction with social distancing as a policy, yet there is little prior work aimed at measuring community acceptance of social distancing. In this paper, we propose a new approach to measuring attitudes towards social distancing by using social media and sentiment analysis. Over a four-month period, we found that 82.5 percent of tweets were in favour of social distancing. The results indicate a widespread acceptance of social distancing in a selected community. We examine options for estimating the optimal (minimal) social distance required at scale, and the implications for securing widespread community support and for appropriate crisis management during emergency health events.