Local response to the SARS-CoV-2 pandemic differed spatially across the United States but the drivers of this spatial variation remain unclear. We approach this open question by studying the relationship between the growth rate of subsequent waves of the pandemic at the county level during the first year of the pandemic, asking whether state or county demographics better explain variation in this relationship. We found clear spatiotemporal patterns in the relationship between the slopes of subsequent waves in a given county. Generally the standardized difference between the growth rates of waves 1 and 2 and waves 2 and 3 were strongly positively correlated over short distances and shifted to a weak negative correlation at intermediate distances. We also found that peer county health group (a categorization of counties by demographic information relevant to public health) explained variation in response better between wave 1 and 2, while state identity was most important between wave 2 and 3. Taken together, we suggest that there are identifiable spatial patterns in pandemic response across the US but that the nature of these patterns change over the course of the pandemic.