Abstract A carbon border adjustment mechanism (CBAM) is a policy that increases the cost of carbon-intensive imports from countries with no or weak national carbon regulation. Proponents advocate that it helps avoid industrial relocation and protects jobs in the importing country; its critics say that it impedes free trade and drives up prices. Despite European Union legislation to introduce a CBAM policy, we find that citizens in our samples across four European countries---Germany (n=3,500), Hungary (n=2,512), Switzerland (n=2,500), and the United Kingdom (n=2,500)---have not formed clear opinions about the policy yet. Results from survey experiments, conducted over the course of 1.5~years, show a strong dislike for price increases associated with a carbon border tax, while the prospect of job protection does little to increase CBAM support---not even among subgroups most affected by import competition. However, employment effects become relevant when we prompt survey respondents to assess the effects of the carbon border tax for their country as a whole instead of for themselves as individuals. Consistent with exploratory findings that right-leaning voters express a much stronger opposition to the CBAM policy, our results speak to growing evidence of the politically polarizing nature of costly, green policies when citizens have not formed clear opinions about a policy yet.