To persist, species are expected to shift their geographical ranges polewards or to higher elevations as the Earth's climate warms. However, although many species' ranges have shifted in historical times, many others have not, or have shifted only at the high-latitude or high-elevation limits, leading to range expansions rather than contractions. Given these idiosyncratic responses to climate warming, and their varied implications for species' vulnerability to climate change, a critical task is to understand why some species have not shifted their ranges, particularly at the equatorial or low-elevation limits, and whether such resilience will last as warming continues. Here we show that compensatory changes in demographic rates are buffering southern populations of two North American tundra plants against the negative effects of a warming climate, slowing their northward range shifts, but that this buffering is unlikely to continue indefinitely. Southern populations of both species showed lower survival and recruitment but higher growth of individual plants, possibly owing to longer, warmer growing seasons. Because of these and other compensatory changes, the population growth rates of southern populations are not at present lower than those of northern ones. However, continued warming may yet prove detrimental, as most demographic rates that improved in moderately warmer years declined in the warmest years, with the potential to drive future population declines. Our results emphasize the need for long-term, range-wide measurement of all population processes to detect demographic compensation and to identify nonlinear responses that may lead to sudden range shifts as climatic tipping points are exceeded.