Using atomic and molecular gas observations from the GASS and COLD GASS surveys and complementary optical/UV data from the Sloan Digital Sky Survey and the Galaxy Evolution Explorer, we investigate the nature of the variations in the molecular gas depletion time observed across the local massive galaxy population. The large and unbiased COLD GASS sample allows us for the first time to statistically assess the relative importance of galaxy interactions, bar instabilities, morphologies, and the presence of active galactic nuclei (AGNs) in regulating star formation efficiency. We find that both the H2 mass fraction and depletion time vary as a function of the distance of a galaxy from the main sequence traced by star-forming galaxies in the SFR-M * plane. The longest gas depletion times are found in below-main-sequence bulge-dominated galaxies (μ*>5 × 108 M ⊙kpc-2, C > 2.6) that are either gas-poor (/M *1010 M ⊙, we derive a global Kennicutt-Schmidt star formation relation of slope 1.18 ± 0.24 and observe structure within the scatter around this relation, with galaxies having low (high) stellar mass surface densities lying systematically above (below) the mean relation, suggesting that is not the only parameter driving the global star formation ability of a galaxy. © © 2012. The American Astronomical Society. All rights reserved..