Abstract Through the lens of administrative burden and ordeals, we investigate challenges that low‐income families face in accessing health and human services critical for their children's healthy development. We employ a mixed methods approach—drawing on administrative data on economically disadvantaged children in Tennessee, publicly available data on resource allocations and expenditures, and data collected in purposive and randomly sampled interviews with public and nonprofit agencies across the state—to analyze the distribution of resources relative to children's needs and provide rich descriptions of the experiences of organizations striving to overcome administrative burdens and support families. We also scrutinize the place‐based resource deserts and environmental contexts of resource gaps and deficiencies in public policies governing the distribution of public resources that exacerbate administrative burdens and inequities in access to public resources. Our insights into the costs imposed on individuals and organizations and how they impede or spill over into other aspects of organizational work point to specific state and local program and policy changes that could be implemented to address resource constraints and alleviate burdens on organizations and poor families.