Medium-resolution spectra from 3650 angstroms to 10,000 angstroms are presented for 96 giant H II regions distributed in 20 spiral galaxies. We have calculated two separate grids of photoionization models, adopting single-star atmospheres (Kurucz) and star clusters synthesized with different Initial Mass Functions (IMFs) as ionizing sources. Additional models were computed with more recent non-LTE stellar atmospheres. We use the radiation softness parameter eta of Vilchez and Pagel to test for a metallicity dependence of the effective temperatures of the ionizing stars. Our results are consistent with a significant decrease in mean stellar temperatures of the ionizing stars with increasing metallicity. The magnitude of the effect, combined with the behavior of the HeI 5876/Hbeta ratio, suggest a smaller upper mass limit for star formation at abundances higher than solar, even when considering the effects of metallicity on stellar evolution and atmospheric line blanketing. However, the exact magnitudes of the stellar temperature and IMF variations are dependent on the choice of stellar atmosphere and evolution models used, as well as on uncertainties in the nebular abundance scale at high metallicities. Our results also constrain the systematic behavior of the ionization parameter and the N/O ratio in extragalactic H II regions. The observed spectral sequences are inconsistent with current stellar evolution models which predict a luminous, hot W-R stellar population in evolved H II regions older than 2-3 Myr. This suggests either that the hardness of the emitted Lyman continuum spectrum has been overestimated in the models, or that some mechanism disrupts the H II regions before the W-R phases become important.