Conventional neo-Darwinian theory views organisms as infinitely sensitive and responsive to their environments, and considers them able to readily change size or shape when they adapt to selective pressures. Yet since 1863 it has been well known that Pleistocene animals and plants do not show much morphological change or speciation in response to the glacial-interglacial climate cycles. We tested this hypothesis with all of the common birds (condors, golden and bald eagles, turkeys, caracaras) and mammals (dire wolves, saber-toothed cats, giant lions, horses, camels, bison, and ground sloths) from Rancho La Brea tar pits in Los Angeles, California, which preserves large samples of many bones from many well-dated pits spanning the 35,000 years of the Last Glacial-Interglacial cycle. Pollen evidence showed the climate changed from chaparral/oaks 35,000 years ago to snowy piñon-juniper forests at the peak glacial 20,000 years ago, then back to the modern chaparral since the glacial-interglacial transition. Based on Bergmann's rule, we would expect peak glacial specimens to have larger body sizes, and based on Allen's rule, peak glacial samples should have shorter and more robust limbs. Yet statistical analysis (ANOVA for parametric samples; Kruskal-Wallis test for non-parametric samples) showed that none of the Pleistocene pit samples is statistically distinct from the rest, indicating complete stasis from 35 ka to 9 ka. The sole exception was the Pit 13 sample of dire wolves (16 ka), which was significantly smaller than the rest, but this did not occur in response to climate change. We also performed a time series analysis of the pit samples. None showed directional change; all were either static or showed a random walk. Thus, the data show that birds and mammals at Rancho La Brea show complete stasis and were unresponsive to the major climate change that occurred at 20 ka, consistent with other studies of Pleistocene animals and plants. Most explanations for such stasis (stabilizing selection, canalization) fail in this setting where climate is changing. One possible explanation is that most large birds and mammals are very broadly adapted and relatively insensitive to changes in their environments, although even the small mammals of the Pleistocene show stasis during climate change, too.