Unitary-resource models posit a collective attentional resource responsible for sustaining information processing across all modalities. In contrast, multiple-resource models presume a system of modality-independent resources. The two models predict similar within-modal performance, but seemingly contradictory cross-modal performance. Discordant outcomes in past research are here hypothesized to result from inconsistent levels of cognitive load imposed within experimental tasks. Participants monitored two simultaneously presented alphabetic letter arrays consisting of the serial presentation of a target and multiple distractors. The dual-task design required the identification of targets in within-modal and cross-modal trials. Cognitive load was manipulated by altering the presentation rate of the letters. While cross-modal performance was generally superior and cognitive load was associated with decreasing performance, the cross-modal advantage prominent at low levels of cognitive load was absent under high cognitive load. Therefore, neither resource model can alone account for dual-task processing, suggesting the role of a hierarchical resource model.