While recent research highlights the potential of social robots to support mood regulation, little is known about how prospective users view their integration into everyday life. To explore this, we conducted an exploratory case study that used a speculative robot concept—Mora—to provoke reflection and facilitate meaningful discussion about using social robots to manage subtle, day-to-day emotional experiences. We focused on the “Sunday Blues,” a common dip in mood that occurs at the end of the weekend, as a relatable context in which to explore individuals’ insights. Using a video prototype and a co-constructing stories method, we engaged 15 participants in imagining interactions with Mora and discussing their expectations, doubts, and concerns. The study surfaced a range of nuanced reflections around the attributes of social robots like empathy, intervention effectiveness, and ethical boundaries, which we translated into design considerations for future research and development in human-robot interaction.