We examine characteristics and correlates of households in the United States that are most likely to have children at risk of inadequate nutrition - those that report very low food security (VLFS) among their children. Using 11 years of the Current Population Survey, plus data from the National Health and Nutrition Examination Survey (NHANES), we describe these households in great detail with the goal of trying to understand how these households differ from households without such severe food insecurity. While household income certainly plays an important role in determining VLFS among children, we find that even after flexibly controlling for income-to-poverty rates some household characteristics and patterns of program participation have important additional explanatory power. Finally, our examination of the NHANES data suggests an important role for both mental and physical health of adults in the household in determining the food security status of children.