Previous research suggests that smartphone users experience strong social pressure to be permanently accessible, but that this need not necessarily become a burden. Up to now, little attention has been paid to differences in the responsiveness to accessibility demands. The present study aims to close this gap by examining how social pressure to be accessible affects perceived stress and well-being. Drawing on self-determination theory and transactional theory of stress, it investigated the underlying motivational processes of smartphone use. A two-day field experiment (N = 61) was conducted to test whether the effects of social pressure (extrinsic motivation) on well-being and stress are mediated by the fulfillment of the intrinsic needs for autonomy, competence, and relatedness, through smartphone use. The results show that social pressure negatively affected autonomy and competence need satisfaction, but that it had no significant impact on relatedness. As expected, social pressure did not directly influence stress or well-being. Overall, social pressure and its resulting effects on need fulfillment strongly influenced how the participants generally felt during the days of the study. It led to higher stress levels, lower perceived vitality, less positive and more negative affect. The findings are discussed in light of current research on the “always on” culture and with regard to its theoretical and practical implications.