Although cellular reprogramming continues to generate new cell types, reprogramming remains a rare cellular event. The molecular mechanisms that limit reprogramming, particularly to somatic lineages, remain unclear. By examining fibroblast-to-motor neuron conversion, we identify a previously unappreciated dynamic between transcription and replication that determines reprogramming competency. Transcription factor overexpression forces most cells into states that are refractory to reprogramming and are characterized by either hypertranscription with little cell division, or hyperproliferation with low transcription. We identify genetic and chemical factors that dramatically increase the number of cells capable of both hypertranscription and hyperproliferation. Hypertranscribing, hyperproliferating cells reprogram at 100-fold higher, near-deterministic rates. We demonstrate that elevated topoisomerase expression endows cells with privileged reprogramming capacity, suggesting that biophysical constraints limit cellular reprogramming to rare events.