How do people view governmental pandemic surveillance? And how can their views inform courts considering the constitutionality of digital monitoring programs aimed at containing the spread of a highly contagious diseases? We measure the perceived intrusiveness of pandemic surveillance through two nationally representative surveys of Americans. Our results show that even at the height of a pandemic people find surveillance for public health to be more intrusive than surveillance for traditional law enforcement purposes. To account for these strong privacy concerns, we propose safeguards that we believe would make cell phone location tracking and other similar digital monitoring regimes constitutionally reasonable.