Large language models (LLMs) have received lots of attention for their impressive performance in in-context dialogues and their potential to revolutionize service industries with a new business model, Model-as-a-Service (MaaS). Automated data labeling is a natural and promising service. However, labeling data with LLMs faces two main challenges: 1) the labels from LLMs may contain uncertainty, and 2) using LLMs for data labeling tasks can be prohibitively expensive, as the scales of datasets are usually tremendous. In this paper, we propose a hierarchical framework named LMCrowd that leverages multiple LLMs for efficient data labeling under budget constraints. The proposed LMCrowd framework first aggregates labels from multiple freely available LLMs, and then employs a large, paid MaaS LLM for relabeling selected instances. Furthermore, we formalize the core process as an optimization problem, aiming to select the optimal set of instances for relabeling by the MaaS LLM, given the current belief state. Extensive experimental evaluations across various real-world datasets demonstrate that our framework outperforms human labelers and GPT-4 in terms of both accuracy and efficiency.