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We present Arecibo 21 cm spectroscopy, Keck HIRES Hb spectroscopy, and WIYN R-band imaging of 11 nearby blue compact galaxies with eective B-band surface brightnesses of SBe \ 19.4È21.2 mag arcsec~2 and eective radii of kpc. This sample was selected to test the reliability of massReff \ 0.6È1.9estimates derived using optical emission line widths, particularly for the blue compact star-forming gal-axies observed at intermediate redshifts (0.1 \ z \ 1). In addition, we also measure the H I content and gas depletion timescales for the nearby blue compact galaxies in an attempt to infer the present nature and possible future evolution of their intermediate-redshift analogs. We detected H I in 10 of 11 sample galaxies. They have H I masses of 0.3È4] 109 H I line widths, of 133È249 km s~1, dynamicalM _, W20,masses of 0.5 to 5] 1010 gas depletion timescales, of 0.3È7 Gyr, H I mass fractions of 0.01ÈM _, qgas,0.58, and mass-to-light ratios of 0.1È0.8. These values span the range of values typical of nearby H II galaxies, irregulars, and spirals. Despite the restricted morphological selection, our sample of galaxies is quite heterogeneous in terms of H I content, dynamical mass, and gas depletion timescale. Therefore, these galaxies have a variety of evolutionary paths and should look very dierent from each other in 5 Gyr. Those with high masses and gas depletion timescales are likely to retain their interstellar medium for future star formation, while the lower mass objects with small gas depletion timescales may be under