American Southwest (ASW) megadroughts represent decadal-scale periods of dry conditions, the near-term risks of which arise from natural low-frequency hydroclimate variability and anthropogenic forcing. A large single-climate-model ensemble indicates anthropogenic forcing increases near-term ASW megadrought risk by a factor of 100, however, accurate risk assessment remains a challenge. At the global-scale we find that anthropogenic forcing may alter the variability driving megadroughts over 55% of land-areas, undermining accurate assessments of their risk. For the remaining areas, current ensembles are too small to characterize megadroughts' driving variability. For example, constraining uncertainty in near-term ASW megadrought risk to 5 percentage points with high confidence requires 287 simulations. Such ensemble sizes are beyond current computational and storage resources and these limitations suggest that constraining errors in near-term megadrought risk projections with high confidence-even in places where underlying variability is stationary-is not currently possible.