We present Arecibo 21 cm spectroscopy, Keck HIRES Hb spectroscopy, and WIYN R-band images of 11 nearby blue compact galaxies selected to be similar to blue compact star-forming galaxies at intermediate redshifts (0.1<z<1). We detect HI in 10 of 11 sample galaxies, yielding HI masses of 0.3-4x10^9 M_odot, HI linewidths, W_20, of 133-249 km/s, dynamical masses of 0.5-5x10^10 M_odot, gas depletion timescales, tau_gas, of 0.3-7 Gyr, HI mass fractions of 0.01-0.58, and mass-to-light ratios of 0.1-0.8. These values span the range typical of nearby HII galaxies, irregulars and spirals. Despite the restricted morphological selection, our sample is quite heterogeneous in HI content, dynamical mass, and gas depletion timescale. Therefore, these galaxies should look very different from each other in 5 Gyr. Fading of intermediate-z luminous blue compact galaxies into NGC-type spheroidals is a viable evolutionary scenario for the least massive, most gas-poor objects. The most consistent characteristic of our sample is that the ratio, R, of HII linewidth to HI 21 cm linewidth (W_20) are systematically less than unity. The simplest explanation is that the ionized gas is more centrally concentrated than the neutral gas within the gravitational potential. On average R=0.66 +/- 0.16, similar to findings for local HII galaxies. We find R is also a function of linewidth; smaller linewidth galaxies have smaller values of R. Correcting optical linewidths by this factor raises derived masses and places these galaxies on the local luminosity--linewidth (Tully-Fisher) relation. If this ratio applies to intermediate-redshift galaxies, then the proposed luminosity evolution of the Tully-Fisher relation is much smaller and more gradual than suggested by studies using optical emission-linewidth measurements.
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