The Deepwater Horizon disaster released 4.9 million barrels of oil into the Gulf of Mexico. Despite clear evidence of exposure and toxicity, there has been little evidence of population-level declines of most nearshore fish and invertebrate populations. Several hypotheses have been proposed to explain this paradox. Two possibilities include a fishing moratorium following the spill and reductions in predation pressure following predator die-offs. We tested both using mass-balance food web models to quantify direct and indirect population sensitivity to perturbations in fishing pressure and bird and dolphin mortality. In doing so, we developed a new method allowing us to quantify responses of one functional group to changes in fishing pressure across all fished groups. We inferred support for a compensatory mechanism, either release from fishing or predation, when the magnitude of modeled population increases following perturbations in fishing or predation far exceeded observations. We found the fishing moratorium to be the most likely potential mitigating mechanism, especially for penaeid shrimp, menhaden, and blue crabs. Dolphin mortality may explain the stability of small sciaenids. Increased seabird mortality did not lead to major changes in any functional group we examined. The consideration of indirect trophic pathways within the food web model produced a wide range of plausible population responses, especially responses to increases in predator mortality. Broadly, this work shows that oil spills are one driver of population dynamics within a broader socioecological system, and understanding oil spill impacts on populations requires consideration of this complexity.