Most animals forage in nutritionally complicated environments in which the densities of complementary foods vary in space and time. Locally rare foods can lead to nutritional deficiencies in consumers, yet there has been little consideration of the influence of nutritional deficits, and consumers’ efforts to redress these deficits, on population and community dynamics. A taxonomically and trophically diverse group of animals can redress accumulated deficits using nutrient-specific foraging, defined here as the ability of an animal to bias its foraging effort towards certain foods on the basis of its own nutritional state. We focus on the true omnivores, because they feed on vastly different nutrient sources, animals and plants. We use an ordinary differential equation model to show that nutrient-specific foraging may destabilize omnivore–prey population dynamics, depending on the degree to which the omnivore alters its foraging in an attempt to balance its nutritional state. In particular, a high behavioral sensitivity to nutritional imbalances led to a novel type of Allee effect driven by the interaction between prey density and nutritional deficiencies in the omnivore. Our model overall is characterized by a causal loop between the omnivore's nutritional state, food preferences and population dynamics. Consequently, the omnivore exhibited a dynamic functional response, in which the relationship between prey density and omnivore per capita consumption of prey was influenced by the current nutritional state of the omnivore. With regards to omnivory in general, our results reinforce the idea that statements about the effects of omnivory on population or community stability are not possible without a consideration of the behavioral mechanisms of diet mixing.