During Pleistocene glacial-interglacial cycles, the geographic range is often assumed to have shifted as a species tracks its climatic niche. Alternatively, the geographic range would not necessarily shift if a species can adapt in situ to a changing environment. The potential for a species to persist in place might increase with the diversity of habitat types that a species exploits. We evaluate evidence for either range shift or range stability between the last glacial maximum (LGM) and present time in the chisel-toothed kangaroo rat (Dipodomys microps), an endemic of the Great Basin and Mojave deserts. We modeled how the species’ range would have changed if the climatic niche of the species remained conserved between the LGM and present time. The climatic models imply that if D. microps inhabited the same climatic niche during the LGM as it does today, the species would have persisted primarily within the warm Mojave Desert and expanded northwards into the cold Great Basin only after the LGM. Contrary to the climatic models, the mitochondrial DNA assessment revealed signals of population persistence within the current distribution of the species throughout at least the latest glacial-interglacial cycle. We concluded that D. microps did not track its climatic niche during late Pleistocene oscillations, but rather met the challenge of a changing environment by shifting its niche and retaining large portions of its distribution. We speculate that this kind of response to fluctuating climate was possible because of ‘niche drifting’, an alteration of the species’ realized niche due to plasticity in various biological characters. Our study provides an example of an approach to reconstruct species’ responses to past climatic changes that can be used to evaluate whether and to what extent taxa have capacity to shift their niches in response to the changing environment – information becoming increasingly important to predicting biotic responses to future environmental changes.