Prior research suggests that cognitive control can assist the comprehension of sentences that create conflict between interpretations, at least under some circumstances. However, the mixed pattern of results suggests that cognitive control may not always be necessary for accurate comprehension. We tested whether cognitive control recruitment for language processing is systematically variable, depending on the type of sentential ambiguity or conflict, individual differences in cognitive control, and task demands. Participants completed two sessions in a web-based experiment. The first session tested conflict modulation using interleaved Stroop and sentence comprehension trials. Critical sentences contained syntax-semantics or phrase-attachment conflict. In the second session, participants completed three cognitive control and three working memory tasks. Exploratory factor analysis was used to index individual differences in a cognitive control factor and a working memory factor. At the group level, there were no significant conflict modulation effects for either syntax-semantics or phrase-attachment conflict. At the individual differences level, the cognitive control factor correlated with offline comprehension accuracy but not online processing measures for both types of conflict. Together, the results suggest that the role of cognitive control in sentence processing may vary according to task demands. When overt decisions are required, individual differences in cognitive control may matter such that better cognitive control results in better language comprehension performance. The results add to the mixed evidence on conflict modulation and raise questions about the situations under which cognitive control influences online processing.