Projected effects of climate change across many ecosystems globally include more frequent disturbance by fire and reduced plant growth due to warmer (and especially drier) conditions. Such changes affect species - particularly fire-intolerant woody plants - by simultaneously reducing recruitment, growth, and survival. Collectively, these mechanisms may narrow the fire interval window compatible with population persistence, driving species to extirpation or extinction. We present a conceptual model of these combined effects, based on synthesis of the known impacts of climate change and altered fire regimes on plant demography, and describe a syndrome we term "interval squeeze". This model predicts that interval squeeze will increase woody plant extinction risk and change ecosystem structure, composition, and carbon storage, especially in regions projected to become both warmer and drier. These predicted changes demand new approaches to fire management that will maximize the in situ adaptive capacity of species to respond to climate change and fire regime change.