Carbon budgets are quantifications of the total amount of carbon dioxide that can ever be emitted while keeping global warming below specific temperature limits. However, estimates of these budgets for limiting warming to 1.5 °C and well-below 2 °C include assumptions about how much warming can be expected from non-CO2 emissions. Here, we uncover the non-CO2 emissions assumptions that underlie the latest remaining carbon budget estimates by the Intergovernmental Panel on Climate Change and quantify the implication of the world pursuing alternative higher or lower emissions. We consider contributions of methane, nitrous oxide, fluorinated gases, and aerosols and show how pursuing inadequate methane emission reductions causes remaining carbon budgets compatible with the Paris Agreement temperature limits to be exhausted today, effectively putting achievement of the Paris Agreement out of reach.