We investigate theoretically the switching characteristics of semiconducting carbon nanotubes connected to gold electrodes under an external (gate) electric field. We find that the external introduction of holes is necessary to account for the experimental observations. We identify metal-induced-gap states (MIGS) at the contacts and find that the MIGS of an undoped tube would not significantly affect the switching behavior, even for very short tube lengths. We also explore the miniaturization limits of nanotube transistors, and, on the basis of their switching ratio, we conclude that transistors with channels as short as 50AA would have adequate switching characteristics.