Cancer cells enter a reversible drug-tolerant persister (DTP) state to evade death from chemotherapy and targeted agents. It is increasingly appreciated that DTPs are important drivers of therapy failure and tumor relapse. We combined cellular barcoding and mathematical modeling in patient-derived colorectal cancer models to identify and characterize DTPs in response to chemotherapy. Barcode analysis revealed no loss of clonal complexity of tumors that entered the DTP state and recurred following treatment cessation. Our data fit a mathematical model where all cancer cells, and not a small subpopulation, possess an equipotent capacity to become DTPs. Mechanistically, we determined that DTPs display remarkable transcriptional and functional similarities to diapause, a reversible state of suspended embryonic development triggered by unfavorable environmental conditions. Our study provides insight into how cancer cells use a developmentally conserved mechanism to drive the DTP state, pointing to novel therapeutic opportunities to target DTPs.