In carbon capture and storage (CCS), CO2 is captured at power plants and then injected underground into reservoirs like deep saline aquifers for long-term storage. While CCS may be critical for the continued use of fossil fuels in a carbon-constrained world, the deployment of CCS has been hindered by uncertainty in geologic storage capacities and sustainable injection rates, which has contributed to the absence of concerted government policy. Here, we clarify the potential of CCS to mitigate emissions in the United States by developing a storage-capacity supply curve that, unlike current large-scale capacity estimates, is derived from the fluid mechanics of CO2 injection and trapping and incorporates injection-rate constraints. We show that storage supply is a dynamic quantity that grows with the duration of CCS, and we interpret the lifetime of CCS as the time for which the storage supply curve exceeds the storage demand curve from CO2 production. We show that in the United States, if CO2 production from power generation continues to rise at recent rates, then CCS can store enough CO2 to stabilize emissions at current levels for at least 100 y. This result suggests that the large-scale implementation of CCS is a geologically viable climate-change mitigation option in the United States over the next century.