Broad bandwidth, infrared light sources have the potential to revolutionize inertial confinement fusion (ICF) by suppressing laser-plasma instabilities. There is, however, a tradeoff: The broad bandwidth precludes high efficiency conversion to the ultraviolet, where laser-plasma interactions are weaker. Operation in the infrared could intensify the role of resonance absorption, an effect long suspected to be the shortcoming of early ICF experiments. Here we present simulations exploring the effect of bandwidth on resonance absorption. In the linear regime, bandwidth has little effect on resonance absorption; in the nonlinear regime, bandwidth suppresses enhanced absorption resulting from the electromagnetic decay instability. These findings evince that regardless of bandwidth, an ICF implosion will confront at least linear levels of resonance absorption.