Public sentiment (the opinions, attitudes or feelings expressed by the public) is a factor of interest for government, as it directly influences the implementation of policies. Given the unprecedented nature of the COVID-19 crisis, having an up-to-date representation of public sentiment on governmental measures and announcements is crucial. While the 'staying-at-home' policy makes face-to-face interactions and interviews challenging, analysing real-time Twitter data that reflects public opinion toward policy measures is a cost-effective way to access public sentiment. In this context, we collect streaming data using the Twitter API starting from the COVID-19 outbreak in the Netherlands in February 2020, and track Dutch general public reactions on governmental measures and announcements. We provide temporal analysis of tweet frequency and public sentiment over the past seven months. We also identify public attitudes towards two Dutch policies in case studies: one regarding social distancing and one regarding wearing face masks. By presenting those preliminary results, we aim to provide visibility into the social media discussions around COVID-19 to the general public, scientists and policy makers. The data collection and analysis will be updated and expanded over time.