Accurate modeling of the spatial accessibility of health care is critical to measuring and responding to physician shortages. We develop a new model in which patients choose the primary care location that minimizes their combined accessibility and availability costs. This model offers several advantages with respect to existing access frameworks. It incorporates feedback between patient decisions and endogenizes the trade-off between travel times and congestion at the point of care. It allows for patients to seek care from their home or workplace and can account for multiple travel modes. Our open-sourced implementation scales efficiently to large areas and fine spatial granularity. Using distributed computing, we calculate travel times for this model at the census tract level for the entire United States, and we also make this resource available. We compare the results to those from existing primary care access models. Key Words: floating catchment areas, primary health care, rational agent models, spatial accessibility.