We study how Generative AI (GenAI) adoption is reshaping work. While prior studies show that GenAI enhances role-level productivity and task composition, its influence on skills - the fundamental enablers of task execution, and the ultimate basis for employability - is less understood. Using job postings from 596 US public firms that recruited explicitly for GenAI skills (2022-2024), we analyze how GenAI adoption shifts the demand for workers' domain-specific as well as higher-order (domain-agnostic) skills. Our findings reveal that roles with higher demand for cognitive skills are also more likely to explicitly advertise GenAI tool requirements such as ChatGPT, Copilot, etc. Further, a difference-in-differences analysis shows that the demand for social skills within GenAI adopting roles decreases by 4.5 percent post-ChatGPT launch. As cognitive and social skills are both meta-skills - i.e., they support the acquisition of future task-specific skills - our results suggest that the adoption of GenAI may be altering the trajectories of feasible upskilling.