Adapting video vision-language models (VLMs) is computationally expensive because video inputs produce a large number of visual tokens, making both fine-tuning and inference costly. Although visual token compression can reduce this overhead, direct adaptation on compressed inputs often causes semantic drift and noticeable performance degradation. We present Token-Budget Distillation (TBD), a parameter-efficient fine-tuning framework for adapting video VLMs under a fixed token budget. TBD freezes the pretrained backbone, updates only LoRA adapters, and integrates FlashVID-based visual token compression into the video pathway. To preserve full-token semantics under compression, TBD employs a dual-path teacher-student design, where a full-token teacher provides stable supervision and a compressed student is optimized with task loss, answer-region KL distillation, GT-anchored margin distillation, and reliability-aware KD control. This design enables the student to recover the semantic behavior of the full-token model while remaining efficient under aggressive token reduction. We evaluate TBD on three video VLM backbones, including LLaVA-Video, LLaVA-OneVision, and Qwen3-VL-8B-Instruct, across four video understanding benchmarks. TBD consistently outperforms compression-only baselines under both moderate and aggressive compression. On LLaVA-Video at retention ratio R = 10 percent, TBD preserves 97.0 percent of the Vanilla model's average accuracy; on LLaVA-OneVision at R = 10 percent, it achieves an average score of 58.4 and matches 100.0 percent relative accuracy.

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