With an ever-increasing number of mobile devices competing for our attention, quantifying when, how often, or for how long users visually attend to their devices has emerged as a core challenge in mobile human-computer interaction. Encouraged by recent advances in automatic eye contact detection using machine learning and device-integrated cameras, we provide a fundamental investigation into the feasibility of quantifying visual attention during everyday mobile interactions. We identify core challenges and sources of errors associated with sensing attention on mobile devices in the wild, including the impact of face and eye visibility, the importance of robust head pose estimation, and the need for accurate gaze estimation. Based on this analysis, we propose future research directions and discuss how eye contact detection represents the foundation for exciting new applications towards next-generation pervasive attentive user interfaces.