Because more and more young people are constantly presented with the opportunity to access information and connect to others via their smartphones, they report to be in a state of permanent alertness. In the current study, we define such a state as smartphone vigilance, an awareness that one can always get connected to others in combination with a permanent readiness to respond to incoming smartphone notifications. We hypothesized that constantly resisting the urge to interact with their phones draws on response inhibition, and hence interferes with students’ ability to inhibit prepotent responses in a concurrent task. To test this, we conducted a preregistered experiment, employing a Bayesian sequential sampling design, where we manipulated smartphone visibility and smartphone notifications during a stop-signal task that measures the ability to inhibit prepotent responses. The task was constructed such that we could disentangle response inhibition from action selection. Results show that the mere visibility of a smartphone is sufficient to experience vigilance and distraction, and that this is enhanced when students receive notifications. Curiously enough, these strong experiences were unrelated to stop-signal task performance. These findings raise new questions about when and how smartphones can impact performance.