A key question for infectious disease dynamics is the impact of the climate on future burden. Here, we evaluate the climate drivers of respiratory syncytial virus (RSV), an important determinant of disease in young children. We combine a dataset of county-level observations from the US with state-level observations from Mexico, spanning much of the global range of climatological conditions. Using a combination of nonlinear epidemic models with statistical techniques, we find consistent patterns of climate drivers at a continental scale explaining latitudinal differences in the dynamics and timing of local epidemics. Strikingly, estimated effects of precipitation and humidity on transmission mirror prior results for influenza. We couple our model with projections for future climate, to show that temperature-driven increases to humidity may lead to a northward shift in the dynamic patterns observed and that the likelihood of severe outbreaks of RSV hinges on projections for extreme rainfall.