Our interdisciplinary study investigates how effectively U.S. laws confront the challenges posed by Generative AI to human values. Through an analysis of diverse hypothetical scenarios crafted during an expert workshop, we have identified notable gaps and uncertainties within the existing legal framework regarding the protection of fundamental values, such as privacy, autonomy, dignity, diversity, equity, and physical/mental well-being. Constitutional and civil rights, it appears, may not provide sufficient protection against AI-generated discriminatory outputs. Furthermore, even if we exclude the liability shield provided by Section 230, proving causation for defamation and product liability claims is a challenging endeavor due to the intricate and opaque nature of AI systems. To address the unique and unforeseeable threats posed by Generative AI, we advocate for legal frameworks that evolve to recognize new threats and provide proactive, auditable guidelines to industry stakeholders. Addressing these issues requires deep interdisciplinary collaborations to identify harms, values, and mitigation strategies.