The continuous declining rate of birth may cause severe worldwide problems, including population ageing and demographic imbalance. This paper aims to identify the geographic disparities and potential influential factors of the extreme downward excess of birth rates in the U.S. at the county level from 2003 to 2020. The innovative Bayesian generalized Pareto (GP) quantile regression model is employed for analysing the spatiotemporal pattern of stressful low birth rate and its association with socioeconomic, demographic, and meteorological factors. The optimal stochastic partial differential equation and autoregressive model of order one (SPDE-AR(1)) spatiotemporal structured model is selected based on common Bayesian criteria and scaled threshold weighted continuous ranked probability score, indicating apparent spatial unbalance and deteriorating tendency of falling birth rate. The findings show that elderly, highly educated population structure, city-developed situation, average birth weight, and average age of mother have a significant impact on the stressful downward excess of birth rate, particularly in examples of Charlotte, Sarasota, Collier counties in Florida, and Marin, Santa, Cruuz, San Mateo in California. Conversely, the increasing female proportion and GDP per capita can alleviate the declining birth rate pressure. Our methodology is productive for analysing extreme population stress including but not limited to birth weight and cognitive impairment.