The growing need to integrate information from a large number of diverse sources poses significant scalability challenges for data integration systems. These systems often rely on manually written schema mappings, which are complex, source-specific, and costly to maintain as sources evolve. While recent advances suggest that large language models (LLMs) can assist in automating schema matching by leveraging both structural and natural language cues, key challenges remain. In this paper, we identify three core issues with using LLMs for schema mapping: (1) inconsistent outputs due to sensitivity to input phrasing and structure, which we propose methods to address through sampling and aggregation techniques; (2) the need for more expressive mappings (e.g., GLaV), which strain the limited context windows of LLMs; and (3) the computational cost of repeated LLM calls, which we propose to mitigate through strategies like data type prefiltering.