We have measured the microwave ionization threshold electric fields for ns-state Na Rydberg atoms from n = 24-33 as a function of the duration of the ionizing microwave pulse. Pulses as short as 2.8 ns were used, containing fewer than 25 cycles of 8.55-GHz radiation. While the fields required to produce the onset of ionization were independent of pulse duration and exhibited the n-5 scaling characteristic of ionization by diffusion through higher-energy states, the fields required to produce nearly complete ionization increased dramatically as the pulse was shortened. Additional measurements of the populations of bound states after the shortest microwave pulses showed that up to ~10% of the atoms were excited to states above the initially populated ns state and the adjacent (n -1) manifold of higher angular momentum states, while most were either ionized or remained in these states. From this observation we conclude that the rate-limiting process for ionization is the transition from the initially populated ns state or the adjacent manifold to the next higher manifold, not the diffusion through higher-lying states.