Lethal mutagenesis, the killing of a microbial pathogen with a chemical mutagen, is a potential broad-spectrum antiviral treatment. It operates by raising the genomic mutation rate to the point that the deleterious load causes the population to decline. Its use has been limited to RNA viruses because of their high intrinsic mutation rates. Microbes with DNA genomes, which include many viruses and bacteria, have not been considered for this type of treatment because their low intrinsic mutation rates seem difficult to elevate enough to cause extinction. Surprisingly, models of lethal mutagenesis indicate that bacteria may be candidates for lethal mutagenesis. In contrast to viruses, bacteria reproduce by binary fission, and this property ensures their extinction if subjected to a mutation rate >0.69 deleterious mutations per generation. The extinction threshold is further lowered when bacteria die from environmental causes, such as washout or host clearance. In practice, mutagenesis can require many generations before extinction is achieved, allowing the bacterial population to grow to large absolute numbers before the load of deleterious mutations causes the decline. Therefore, if effective treatment requires rapid population decline, mutation rates >>0.69 may be necessary to achieve treatment success. Implications for the treatment of bacteria with mutagens, for the evolution of mutator strains in bacterial populations, and also for the evolution of mutation rate in cancer are discussed.