Children with sensorineural hearing loss show considerable variability in spoken language outcomes. We tested whether specific deficits in supra-threshold auditory perception might contribute to this variability. In a previous study [Halliday, Rosen, Tuomainen, & Calcus, (2019), J. Acoust. Soc. Am, 146, 4299], children with mild-to-moderate sensorineural hearing loss (MMHL) were shown to perform more poorly than normally hearing (NH) controls on measures designed to assess sensitivity to the temporal fine structure (TFS, the rapid oscillations in the amplitude of narrowband signals over short time intervals). However, they performed within normal limits on measures assessing sensitivity to the envelope (E; the slow fluctuations in the overall amplitude). Here, individual differences in unaided sensitivity to TFS accounted for significant variance in the spoken language abilities of children with MMHL, after controlling for nonverbal IQ, family history of language difficulties, and hearing loss severity. Aided sensitivity to TFS and E cues was equally important for children with MMHL, whereas for children with NH, E cues were more important. These findings suggest that deficits in TFS perception may contribute to the variability in spoken language outcomes in children with sensorineural hearing loss.