Workplace telepressure – an urge to respond quickly to digital work messages – has been linked to negative outcomes for both employee health and organizational effectiveness. However, there is little research investigating factors that help guard workers against the adverse outcomes of telepressure. This study proposes the use of family supportive supervisor behaviors (FSSB) to moderate the relationships between telepressure and two such outcomes: work-family conflict and work burnout. Specifically, employees who work under family-supportive supervisors should experience less work-family conflict and work burnout as a result of telepressure. Archival self-report survey data from 247 full-time American workers confirmed the positive relationships between telepressure, work-family conflict, and work burnout through bivariate correlations. Moderated multiple regressions found that FSSB does not buffer the relationship between telepressure and these two outcomes of interest; rather, it strengthens it. Further exploration into this result found that although FSSB helps lower work-family conflict and burnout in employees experiencing low levels of telepressure, it fails to protect employees high on telepressure from negative outcomes. This research adds to the occupational health literature by highlighting the importance of matching job resources to specific job demands. Organizations may choose to introduce FSSB training to help employees experience less work-family conflict or burnout, but in order to directly guard against telepressure, companies should focus on educating supervisors specifically about healthy technology habits.