Designing climate change policies requires considering the feedback loops between mitigation and adaptation, since more mitigation efforts today will trigger lower adaptation costs. In this framework, carbon taxes are often seen as promising tools but at the risk of financially overburdening the private sector, depriving it of important economic resources. However, analyzing the financial feasibility of mitigation-adaptation policies using conventional Integrated Assessment Models (IAM) is limited, as they do not simultaneously endogenize economic growth, emissions, and damages. Here, we present IDEE (Integrated Dynamic Environment-Economic), a new IAM based on the coupling of an Earth Model of Intermediate Complexity and a non-linear macroeconomic model in continuous time. Then, we analyze the simultaneous effects of carbon taxes and public spending, both on climate and on the world economy. We show that, above a warming about +2.3°C, damages drastically foster the need for additional investments in productive capital—an adaptation necessity—that potentially leads private firms to a debt overhang and a worldwide cascade of defaults. This suggests that the Paris Agreement target should not only be motivated by the climatic non-linearities and tipping points arising beyond the +2°C threshold, but also by the emergence of financial tipping points. We also show that, provided public subsidies are high enough, a tax of USD 300 per tCO2e by 2030 enables reaching net-zero emissions in 2050, preventing firms from suffering global bankruptcy. We anticipate IDEE to be a starting point for a new class of IAMs that better represent the reciprocal feedback loops between the environment and the economy.