Although mass vaccination is the best way out of the pandemic, the share of skeptics is substantial in most countries. Social campaigns can emphasize the many arguments that potentially increase acceptance for vaccines: e.g., that they have been developed, tested, and recommended by doctors and scientists; and that they are safe, effective, and in demand. We verified the effectiveness of such messages in an online experiment conducted in February and March 2021 with a sample of almost six thousand adult Poles, which was nationally representative in terms of key demographic variables. We presented respondents with different sets of information about vaccinating against COVID-19. After reading the information bundle, they indicated whether they would be willing to be vaccinated. We also asked them to justify their answers and indicate who or what might change their opinion. Finally, we elicited a number of individual characteristics and opinions. We found that nearly 45% of the respondents were unwilling to be vaccinated, and none of the popular messages we used was effective in reducing this hesitancy. We also observed a number of significant correlates of vaccination attitudes, with men, older, wealthier, and non-religious individuals, those with higher education, and those trusting science rather than COVID-19 conspiracy theories being more willing to be vaccinated. We discuss important consequences for campaigns aimed at reducing COVID-19 vaccine hesitancy.