Salt marshes are important coastal environments that provide key ecological services. As sea level rise has accelerated globally, concerns about the ability of salt marshes to survive submergence are increasing. Previous estimates of likely survival of salt marshes were based on ratios of sea level rise to marsh platform accretion. Here we took advantage of an unusual, long-term (1979-2015), spatially detailed comparison of changes in a representative New England salt marsh to provide an empirical estimate of habitat losses based on actual measurements. We show prominent changes in habitat mosaic within the marsh, consistent and coincident with increased submergence and coastal erosion. Model results suggest that at current rates of sea level rise, marsh platform accretion, habitat loss, and with the limitation of the widespread "coastal squeeze", the entire ecosystem might disappear by the beginning of the next century, a fate that might be likely for many salt marshes elsewhere. Meta-analysis of available data suggests that 40 to 95% of the world's salt marshes will be submerged, depending on whether sea level rise remains at current or reaches anticipated rates for the end of this century.