Prompt-driven Video Segmentation Foundation Models (VSFMs), such as SAM2, are increasingly used in applications including autonomous driving and digital pathology, yet their security risks remain underexplored. We study backdoor attacks against VSFMs and show that directly applying classic attacks such as BadNet is largely ineffective, yielding attack success rates (ASR) below 5%. Through gradient-similarity and attention-map analyses, we find that traditional backdoor training fails because clean and triggered samples induce aligned image-encoder gradients, while model attention remains focused on the prompt-specified object rather than the trigger. To address this limitation, we propose BadVSFM, the first backdoor attack framework tailored to prompt-driven VSFMs. BadVSFM uses a two-stage strategy that first learns trigger-specific encoder features and then trains the decoder to map triggered frame prompt representations to an attacker-specified target mask while preserving clean segmentation behavior. Experiments on five VSFMs and two datasets show that BadVSFM achieves strong, controllable backdoor effects across triggers and prompt types with limited clean-performance degradation. Ablations and interpretability analyses validate the necessity of the two-stage design, and five representative defenses remain largely ineffective. Our results reveal a practical and underexplored vulnerability of current VSFMs to backdoor threats.