On November 8, 2021, the Danish government held a press conference re-introducing COVID-19 passports both to mitigate the recent surge in COVID-19 infections and to put more pressure on still unvaccinated people to take up the vaccine. The press conference was also notable for the Prime Minister, Mette Frederiksen, condemning the unvaccinated in unprecedentedly harsh words. While new vaccinations increased in the weeks following the press conference, we show that the press conference had unintended, negative consequences. We analyze daily, nationally representative survey data (total N= 25K) employing a difference-in-differences design. We demonstrate that the press conference broadened by 25-33% the already large gaps between vaccinated and unvaccinated citizens on four out of five key psychological antecedents of health compliance. Most notably, we find that trust in the strategy of managing the COVID-19 epidemic decreased by 11 percentage points among the unvaccinated but stayed high among the vaccinated. When considering “pressure” as a pandemic management strategy it is important to be aware of these unintended costs and how they may shape the unvaccinated citizens’ compliance with other health advice and their overarching support for the political system.