We present a mid-infrared spectroscopic data cube of the central part of 30 Doradus, observed with Spitzer's IRS and MIPS/SED mode. Aromatic dust emission features and emission lines from molecular and atomic hydrogen are detected but not particularly strong. The dominant spectral features are emission lines from moderately ionized species of argon, neon, and sulphur, which are used to determine the physical conditions in the ionized gas. The ionized gas excitation shows strong variations on parsec scales, some of which can plausibly be associated with individual hot stars. We fit the ionic line strengths with photoionization and shock models, and find that photoionization dominates in the region. The ionization parameter U traces the rim of the central bubble, as well as highlighting isolated sources of ionization, and at least one quiescent clump. The hardness of the ionizing radiation field T_rad reveals several "hot spots" that are either the result of individual very hot stars or trace the propagation of the diffuse ionizing field through the surrounding neutral cloud. Consistent with other measurements of giant molecular hydrogen regions, log(U) ranges between -3 and -0.75, and T_rad between 30000 and 85000K. ; Comment: 32 pages, 26 figures, ApJ accepted. A version with high-resolution images can be found at http://www.astro.virginia.edu/~ged3j/indebetouw20090125.pdf