Both response selection and visual attention are limited in capacity. According to the central bottleneck model, the response selection processes of two tasks in a dual-task situation are performed sequentially. In conjunction search, visual attention is required to select the items and to bind their features (e.g., color and form), which results in a serial search process. Search time increases as items are added to the search display (i.e., set size effect). When the search display is masked, visual attention deployment is restricted to a brief period of time and target detection decreases as a function of set size. Here, we investigated whether response selection and visual attention (i.e., feature binding) rely on a common or on distinct capacity limitations. In four dual-task experiments, participants completed an auditory Task 1 and a conjunction search Task 2 that were presented with an experimentally modulated temporal interval between them (Stimulus Onset Asynchrony, SOA). In Experiment 1, Task 1 was a two-choice discrimination task and the conjunction search display was not masked. In Experiment 2, the response selection difficulty in Task 1 was increased to a four-choice discrimination and the search task was the same as in Experiment 1. We applied the locus-of-slack method in both experiments to analyze conjunction search time, that is, we compared the set size effects across SOAs. Similar set size effects across SOAs (i.e., additive effects of SOA and set size) would indicate sequential processing of response selection and visual attention. However, a significantly smaller set size effect at short SOA compared to long SOA (i.e., underadditive interaction of SOA and set size) would indicate parallel processing of response selection and visual attention. In both experiments, we found underadditive interactions of SOA and set size. In Experiments 3 and 4, the conjunction search display in Task 2 was masked. Task 1 was the same as in Experiments 1 and 2, respectively. In both experiments, the d′ analysis revealed that response selection did not affect target detection. Overall, Experiments 1–4 indicated that neither the response selection difficulty in the auditory Task 1 (i.e., two-choice vs. four-choice) nor the type of presentation of the search display in Task 2 (i.e., not masked vs. masked) impaired parallel processing of response selection and conjunction search. We concluded that in general, response selection and visual attention (i.e., feature binding) rely on distinct capacity limitations.