Droughts and heat waves have important impacts on multiple sectors including water resources, agriculture, electricity generation, and public health, so it is important to understand how they will be affected by climate change. However, there is large uncertainty in the projected changes of these extreme events from climate models. In this study, historical biases in models are compared against their future projections to understand and attempt to constrain these uncertainties. Biases in precipitation, near-surface air temperature, evapotranspiration, and a land–atmospheric coupling metric are calculated for 24 models from phase 5 of the Coupled Model Intercomparison Project (CMIP5) against 2 models from phase 2 of the North American Land Data Assimilation System (NLDAS-2) as reference for 1979–2005. These biases are highly correlated across variables, with some models being hotter and drier and others wetter and cooler. Models that overestimate summer precipitation project larger increases in precipitation, evapotranspiration, and land–atmospheric coupling over important agricultural regions by the end of the twenty-first century (2070–99) under RCP8.5, although the percentage variance explained is low. Changes in the characteristics of droughts and heat waves are calculated and linked to historical biases in precipitation and temperature. A method to constrain uncertainty by ranking models based on historical performance is discussed but the rankings differ widely depending on the variable considered. Despite the large uncertainty that remains in the magnitude of the changes, there is consensus among models that droughts and heat waves will increase in multiple regions in the United States by the end of the twenty-first century unless climate mitigation actions are taken.