A remaining carbon budget (RCB) estimates how much CO2 we can emit and still reach a specific temperature target. The RCB concept is attractive since it easily communicates to the public and policymakers, but RCBs are also subject to uncertainties. The expected warming levels for a given carbon budget has a wide uncertainty range, which we show here to increase with less ambitious targets, i.e., with higher CO2 emissions and temperatures. We demonstrate that the leading cause of the revealed RCB uncertainty is the spread in the equilibrium climate sensitivity (ECS) among climate models. In the Coupled Model Intercomparison Project Phase 6 (CMIP6) ensemble, the models with the lower ECS predict an RCB that is twice as high as that of models with the higher ECS, for temperature targets between 1.5-3.0°C.