Climate change mitigation policies are becoming more common, but many citizens, despite claiming to be concerned about climate change, show resistance to accepting policies. What factors determine whether a person holds consistent climate attitudes? This article investigates the concern-policy support gap, which occurs when the concern about climate change and the degree of support for a policy are not aligned. Using the literature on exogenous shocks, related to natural disasters and economic crises, it is claimed that people who have been directly impacted more by climate change will have their attitudes more aligned than people who have been less affected. The opposite is happening with people more affected by economic deprivation, who will have less coherence between attitudes than those less affected. But it is not only the exogenous factors that are important; the direct or indirect cost of a policy will be a determining factor in keeping the concern about climate change and the predisposition to accept this measure aligned. In addition, it is expected to find that in those policies that imply a higher cost for the citizen, the coherence between attitudes will be lower. To verify this, a new exclusive panel survey has been used to collect climate attitudes such as assessments of different measures or the degree of concern about climate change. With these data it can be seen that exogenous shocks, economic or climatic, affect the coherence between climatic attitudes, although it is vital to consider the cost of such a policy for the citizen.