Viruses can occasionally emerge by infecting new host species. However, the early phases of emergence can hinge 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 virus extinction before the latter phases of emergence, where genetic adaptations that improve host use may occur. We examined the early phase of emergence by studying the population dynamics of RNA phages in replicated laboratory environments containing native and novel host bacteria. To predict the breadth of transmission rates allowing viral persistence on each species, we developed a simple model based on in vitro data for phage growth rate over a range of initial population densities on both hosts. Validation of these predictions using serial passage experiments revealed a range of transmission rates for which the native host was a source and 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 on the novel host. We argue that this effect should facilitate adaptation by the virus to utilize the novel host--often crucial in subsequent phases of emergence.