How runoff will change as atmospheric CO₂ rises depends upon several difficult to project factors, including CO₂ fertilization, lengthened growing seasons, and vegetation greening. However, geologic records of the hydrological response to past carbon cycle perturbations indicate large increases in runoff with higher CO₂. We demonstrate that the fact that the Earth has remained habitable since life emerged sets a lower-bound on the sensitivity of runoff to CO₂ changes. The recovery of the Earth system from perturbations is attributed to silicate weathering, which transfers CO₂ to the oceans as alkalinity via runoff. Though many factors mediate weathering rates, runoff determines the total flux of silicate-derived cations and hence the removal flux of excess CO₂. Using a carbon cycle model that parameterizes weathering as a function of rock reactivity, runoff, temperature, and soil CO₂, we show that recovery from a perturbation is only possible if the lower-bound for the sensitivity of runoff to atmospheric CO₂ is 0%/K. Using proxy data for the Paleocene-Eocene Thermal Maximum, we find that to match the marine d¹³C record requires a runoff sensitivity greater than 0%/K and similar to estimates of the modern runoff sensitivity derived from an ensemble of Earth system models. These results suggest that the processes that enhance global runoff are likely to prevail over processes that tend to dampen runoff. In turn, that the Earth has always recovered from perturbations suggests that, though the runoff response is spatially complex, global discharge has never declined in response to warming, despite quite varied paleogeographies.