Anticipating species’ responses to environmental change is a pressing mission in biodiversity conservation. Despite decades of research investigating how climate change may affect population sizes, historical context is lacking, and the traits that mediate demographic sensitivity to changing climate remain elusive. We use whole-genome sequence data to reconstruct the demographic histories of 263 bird species over the past million years and identify networks of interacting morphological and life history traits associated with changes in effective population size (Ne) in response to climate warming and cooling. Our results identify direct and indirect effects of key traits representing dispersal, reproduction and survival on long-term demographic responses to climate change, thereby highlighting traits most likely to influence population responses to ongoing climate warming.