We develop a model of parental investment in early childhood in which bandwidth-constrained parents hold distorted beliefs about the returns to responsive interaction. When capacity falls short of aspiration, motivated reasoning provides relief: the parent distorts her working belief downward, rationalizing low engagement. Distorted beliefs suppress responsive parenting, which generates no calibration evidence, which, in turn, confirms the distortion. The model identifies four channels through which interventions escape this self-sealing trap. A randomized controlled trial confirms the model‘s predictions on parental beliefs, measures of responsive parenting, behavioral engagement, and absence of impact on materials or placebo outcomes.