Learning-based policies are being considered to augment the dexterity of human surgeons in robot-assisted surgery. Can the end-to-end mapping from visual observations to robot actions be vulnerable to adversarial attacks, potentially leading to patient injury? In this paper, we present the first study of adversarial threats to learning-based policies in surgical robotics. We investigate two threat modes: (a) disruptive attacks, where imperceptible visual perturbations interrupt policy execution, and (b) steering attacks, where such perturbations steer policy actions toward attacker-specified directions. We formulate three adversarial attack methods, each with increasing access to policy information, and evaluate their impact on two surgical subtasks: debridement and suturing. Our evaluation covers three end-to-end policy architectures: ACT, Diffusion Policy, and Pi0. In addition, we introduce a new class of photometric adversarial attacks that mimic natural visual changes, such as lighting variations, to generate effective yet visually plausible perturbations. Results from 560 physical experiments using phantoms for debridement and suturing suggest that state-of-the-art policies can be significantly disrupted, resulting in an average 61% reduction in surgical subtask success rates. Project page: https://sites.google.com/view/adversary-surgery