Asteroids with low orbital perihelion distances experience extreme heating from the Sun that can modify their surfaces and trigger nontypical activity mechanisms. These objects are generally difficult to observe from ground-based telescopes due to their frequent proximity to the Sun. The Near-Earth Object (NEO) Surveyor mission, however, will regularly survey down to solar elongations of 45° and is well suited for the detection and characterization of low-perihelion asteroids. Here, we use the survey simulation software tools developed for mission verification to explore the expected sensitivity of NEO Surveyor to these objects. We find that NEO Surveyor is expected to be >90% complete for near-Sun objects larger than D ∼ 300 m. Additionally, if the asteroid (3200) Phaethon underwent a disruption event in the past to form the Geminid meteor stream, Surveyor will be >90% complete to any fragments larger than D ∼ 200 m. For probable disruption models, NEO Surveyor would be expected to detect dozens of objects on Phaethon-like orbits, compared to a predicted background population of only a handful of asteroids, setting strong constraints on the likelihood of this scenario.