The widespread availability of personal data on the internet has given rise to significant concerns about the power and reach of state and corporate surveillance of the population. Researchers have suggested that ordinary citizens generally lack knowledge and control over online personal data and this has led to a sense of resignation in relation to such surveillance. This paper conceptualises public attitudes towards state surveillance within Jasanoff’s (2015) “sociotechnical imaginaries” framework and draws on an Australian survey to examine the complexity and contradictory nature of these attitudes in response to hypothetical use cases. Our study provides estimates of the prevalence of competing sociotechnical imaginaries, ranging from sizeable support for the dominant vision that surveillance can prevent/pre-empt crime/terrorism, to smaller but not insignificant support for either a dystopian or an ambivalent vision recognising the risks of such surveillance. Our results also demonstrate how sociotechnical imaginaries vary by demographics, political orientation, and perception of both citizen-state relations and the effectiveness of state surveillance practices.