Few-shot model compression aims to compress a large model into a more compact one with only a tiny training set (even without labels). Block-level pruning has recently emerged as a leading technique in achieving high accuracy and low latency in few-shot CNN compression. But, few-shot compression for Vision Transformers (ViT) remains largely unexplored, which presents a new challenge. In particular, the issue of sparse compression exists in traditional CNN few-shot methods, which can only produce very few compressed models of different model sizes. This paper proposes a novel framework for few-shot ViT compression named DC-ViT. Instead of dropping the entire block, DC-ViT selectively eliminates the attention module while retaining and reusing portions of the MLP module. DC-ViT enables dense compression, which outputs numerous compressed models that densely populate the range of model complexity. DC-ViT outperforms state-of-the-art few-shot compression methods by a significant margin of 10 percentage points, along with lower latency in the compression of ViT and its variants.