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Advances in 3D generative AI have enabled the creation of physical objects from text prompts, but challenges remain in creating objects involving multiple component types. We present a pipeline that integrates 3D generative AI with vision-language models (VLMs) to enable the robotic assembly of multi-component objects from natural language. Our method leverages VLMs for zero-shot, multi-modal reasoning about geometry and functionality to decompose AI-generated meshes into multi-component 3D models using predefined structural and panel components. We demonstrate that a VLM is capable of determining which mesh regions need panel components in addition to structural components based on object functionality. Evaluation across test objects shows that users preferred the VLM-generated assignments 90.6\% of the time, compared to 59.4\% for rule-based and 2.5\% for random assignment. Lastly, the system allows users to refine component assignments through conversational feedback, enabling greater human control and agency in making physical objects with generative AI and robotics.