To what extent can worldwide carbon pricing foster the transition towards a low-carbon economy and mitigate the effects of global warming? We address this question by assessing the financial impacts and macroeconomic implications of carbon pricing and public subsidies. More specifically, we evaluate the extent to which such policies are sustainable by computing the probability of remaining below two thresholds that we argue to be indicative of the stability of our current economy and climate: (1) a temperature anomaly above +2°C (a commonly acknowledged target, including in the 2015 Paris Agreement, to potentially avoid nonlinearities in the climate system) and (2) a large global debt-to-output ratio of 270%.