Viruses can occasionally emerge by infecting new host species. However, the first phase of emergence hinges upon ecological sustainability of the virus population, which is a product of both within-host population growth and between-host transmission. Insufficient growth or transmission can force extinction of the virus population prior to the second phase of emergence, characterized by genetic adaptations that improve host use. We examined the primary phase of emergence by studying the population dynamics of RNA phages in replicated laboratory environments containing native and novel host bacteria. We developed a simple model based on in vitro data for phage growth rate over a range of initial population densities on both hosts, to predict the breadth of transmission rates allowing viral persistence on each species. Validation of these predictions using serial passage experiments revealed a range of transmission rates for which the native host was a source while the novel host was a sink. In this critical range of transmission rates, periodic exposure to the native host was sufficient for the maintenance of the viral population at high abundance on the novel host. We argue that this effect should facilitate adaptive evolution by the virus to utilize the novel host - a crucial second phase of emergence.