All near-Earth asteroids (NEAs) that reach sufficiently small perihelion distances will undergo a so-called super-catastrophic disruption. The mechanisms causing such disruptions are currently unknown or, at least, undetermined. To help guide theoretical and experimental work to understand the disruption mechanism, we use numerical simulations of a synthetic NEA population to identify the resonant mechanisms that are responsible for driving NEAs close to the Sun, determine how these different mechanisms relate to their dynamical lifetimes at small heliocentric distances and calculate the average time they spend at different heliocentric distances. Typically, resonances between NEAs and the terrestrial and giant planets are able to dramatically reduce the perihelion distances of the former. We developed an algorithm that scans the orbital evolution of asteroids and automatically identifies occurrences of mean motion and secular resonances. We find that most near-Sun asteroids are pushed to small perihelion distances by the 3:1J and 4:1J mean-motion resonances with Jupiter, as well as the secular resonances ν6, ν5, ν3, and ν4. The time-scale of the small-perihelion evolution is fastest for the 4:1J, followed by the 3:1J, whereas ν5 is the slowest. Approximately 7 per cent of the test asteroids were not trapped in a resonance during the latest stages of their dynamical evolution, which suggests that the secular oscillation of the eccentricity due to the Kozai mechanism, a planetary close encounter, or a resonance that we have not identified pushed them below the estimated average disruption distance.