The high relief of the modern Rocky Mountain landscape formed in the late Cenozoic by downcutting of a fluvial network that links a series of easily eroded sedimentary basins across relatively resistant crystalline cores of adjacent ranges. Using a numerical model of fluvial erosion and the flexural isostatic response to the associated unloading, we first calculate the expected pattern and pace of incision caused by rock uplift related to migration of the Yellowstone hot spot and to growth of the northern portion of the Rio Grande rift. Calculated incision rates are <60 m/Myr, and total depth of erosion of sedimentary basins is <300 m, well below the long-term incision rates and amounts of erosion interpreted from the geologic record. Broad-scale tilting of the region toward the east, accomplished by a gradient in rock uplift of ~1 km along the north-south axis of the central Rockies, declining to zero 1000 km to the east, can account for the additional erosion needed to match observations. In each modeling scenario, stream incision is nonsteady, with rock uplift outpacing erosion for <1 Myr in perimeter basins and 1--5 Myr in interior basins. Three factors dominate the spatial and temporal pattern of regional landscape evolution: (1) the time since uplift began, (2) the uplift pattern, and (3) the distribution of relatively resistant bedrock within the region. Our results suggest that the spatial variability in late Cenozoic exhumation can be explained by a long-lived transience in the stream network response to these various late Cenozoic geophysical events.