Multi-agent debate (MAD) systems leverage collaborative interactions among large language models (LLMs) agents to improve reasoning capabilities. While recent studies have focused on increasing the accuracy and scalability of MAD systems, their security vulnerabilities have received limited attention. In this work, we introduce MAD-Spear, a targeted prompt injection attack that compromises a small subset of agents but significantly disrupts the overall MAD process. Manipulated agents produce multiple plausible yet incorrect responses, exploiting LLMs' conformity tendencies to propagate misinformation and degrade consensus quality. Furthermore, the attack can be composed with other strategies, such as communication attacks, to further amplify its impact by increasing the exposure of agents to incorrect responses. To assess MAD's resilience under attack, we propose a formal definition of MAD fault-tolerance and develop a comprehensive evaluation framework that jointly considers accuracy, consensus efficiency, and scalability. Extensive experiments on five benchmark datasets with varying difficulty levels demonstrate that MAD-Spear consistently outperforms the baseline attack in degrading system performance. Additionally, we observe that agent diversity substantially improves MAD performance in mathematical reasoning tasks, which challenges prior work suggesting that agent diversity has minimal impact on performance. These findings highlight the urgent need to improve the security in MAD design.