In cognitive control tasks, participants are presented with stimuli and are instructed to respond to one task-relevant dimension while ignoring another task-irrelevant dimension(s). In such experiments, task conflict reflects the additional effort associated with performing two tasks, such as identifying the color while reading the word in the color-word Stroop task, and is indicated by the difference between conditions that consist of two tasks (congruent and incongruent trials) and conditions that only consist of one task (neutral trials). In a series of three experiments, we used the color-digit Stroop task and manipulated the processing difficulty associated with the irrelevant dimension of the presented stimuli. We found that while information conflict was evident in all conditions, a gradient of task conflict was observed so that the more difficult it was to perceive the task-irrelevant dimension, the stronger task conflict was. We suggest that task conflict is present even when there is no evidence for it and that a critical condition for its appearance is the resources allocated to the irrelevant task. Moreover, these results suggest that our ability to inhibit the involuntary activation of an unwanted process is restricted. Therefore, despite the resource-intensive usage of completing the irrelevant task, it still takes place.