Objective The interdisciplinary literature on social capital has given relatively little attention to the potential downside of social embeddedness. Based on a cross‐national data set (International Social Survey Programme), this study examines how and to what extent social ties and organizational membership are associated with experiencing “too many demands” from close contacts. Methods Hierarchical general linear models are estimated to analyze the linkage between several social capital indicators and the precarious nature of being connected. Results Findings from multilevel analysis indicate that frequency of interaction with friends and relatives, as well as level of involvement in voluntary organizations, are significantly related to feeling burdened because of network‐mediated demands. Conclusion This study suggests that network ties may be viewed as a double‐edged sword. Interpersonal and organizational embeddedness not only produces benefits of social capital but also requires from individual members the necessary obligations and responsibilities associated with it.