Numerical simulations of particles placed in orbital resonances in the main asteroid belt show that the typical dynamical lifetimes of objects that could become near-Earth asteroids or meteorites are only a few million years, with the majority destroyed by being transferred to Jupiter-crossing orbits or being driven into the sun. Particles that fortuitously migrate to the terrestrial planet region may be pushed to high-inclination orbits by resonances but are still dynamically eliminated on time scales of similar to 10 million years, These shorter lifetimes may require a reassessment of our qualitative understanding about near-Earth asteroids and meteorite delivery.