We have calculated the effects of quantum confinement on maximum achievable free carrier concentrations in semiconductor nanowires. Our calculations are based on the amphoteric defect model, which describes the thermodynamic doping limit in semiconductors in terms of the compensation of external dopants by native defects. We find that the generation of amphoteric native defects strongly limits maximum achievable carrier concentrations for nanowires with small widths where quantum confinement is appreciable. The magnitude of this effect in a given material is found to be determined by two material properties: the effective mass of the free carriers, and the position of the conduction (n-type) or valence band (p-type) edge on the absolute energy scale. These results offer a simple, predictive guideline for designing nanostructure devices and contacts where high doping levels are needed.