Carbon taxes evoke a variety of public responses, often with negative implications for policy support, implementation, and stringency. Here we use topic modeling to analyze associations of Spanish citizens with a policy proposal to introduce a carbon tax. This involves asking two key questions, to elicit (1) citizens’ associations with a carbon tax and (2) their judgment of the fairness of such a policy for distinct uses of tax revenues. We identify 11 topics for the first question and 18 topics for the second. We perform regression analysis to assess how respondents’ associations relate to their carbon tax acceptability, knowledge, and sociodemographic characteristics. The results show that, compared to people accepting the carbon tax, those rejecting it show less trust in politicians, think that the rich should pay more than the poor, consider the tax to be less fair, and stress more a lack of renewable energy or low-carbon transport. Respondents accepting a carbon tax emphasize more the need to solve environmental problems and care about a just society. These insights can help policymakers to improve the design and communication of climate policy with the aim to increase its public acceptability.