The response of vegetation gc to changes in moisture availability is a major source of uncertainty in climate projections. While vegetation typically reduces stomatal conductance during drought, accurately modeling how and to what degree stomata respond to changes in moisture availability at global scales is particularly challenging, because no global scale gc observations exist. Here, we leverage a collection of satellite, reanalysis, and station-based near-surface air and surface temperature estimates to develop a novel emergent constraint of drought sensitivity in an ensemble of Earth System Models (ESMs). We find that ESMs systematically underestimate sensitivity. We show that this underestimation occurs because ESMs inadequately reduce gc when soil moisture decreases. As gc controls carbon, water, and energy fluxes, the misrepresentation of modeled sensitivity contributes to biases in ESM projections of gross primary production, transpiration, and temperature during droughts. Our results suggest that the severity and duration of droughts may be misrepresented in ESMs due to the impact of sustained gc on both soil moisture dynamics and the biosphere-atmosphere feedbacks that affect local temperatures and regional weather patterns.