Yu-Hsuan Teng, Alberto D. Bolatto, Peter J. Teuben, Erik Rosolowsky, David T. Frayer, Amanda A. Kepley, Sebastian F. Sanchez, Tony Wong, Adam K. Leroy, Dario Colombo, Serena A. Cronin, K. Decker French, Veselina Kalinova, Rebecca C. Levy, Karin M. Sandstrom, Vicente Villanueva, Jorge K. Barrera-Ballesteros, Zein Bazzi, Yixian Cao, Alex Green, Rodrigo Herrera-Camus, Eduardo A. D. Lacerda, Jialu Li, Alejandra Z. Lugo-Aranda, Jocabed Martinez-Lopez, Elizabeth Tarantino, Akshat Tripathi, Carolyn G. Volpert, Di Wen

We present GBT-EDGE, a new CO(1-0) survey using the Green Bank Telescope to map 62 nearby (10-140 Mpc) galaxies spanning the star-forming main sequence (SFMS), green valley, and red sequence. The galaxy sample is selected from the CALIFA survey with integral field spectroscopy (IFS), which provides a representative census of local galactic environments. Combining the CO dataset with CALIFA's optical IFS measurements, we derive molecular gas masses, star formation rates (SFR), metallicities, and stellar mass densities to measure star formation efficiency (SFE) and investigate the physical drivers of galaxy quenching. We obtain a median molecular gas depletion time of $2.10^{+2.35}_{-1.31}$, $6.90^{+17.00}_{-3.67}$, and $127.7^{+201.6}_{-113.4}$ Gyr for our sample of main sequence, green valley, and red galaxies, respectively, assuming a Galactic CO-to-H2 conversion factor. By applying various conversion factor prescriptions, we also confirm a systematic decrease of SFE with galaxy's offset below the SFMS, regardless of the adopted prescription. This suggests that the low SFR in some quenched galaxies is primarily driven by suppressed SFE rather than an absence of molecular gas. Our results provide evidence that galaxies below the main sequence can retain substantial molecular gas reservoirs comparable to star-forming galaxies, but they exhibit longer depletion times and form stars inefficiently, possibly due to the combined effects of low gas density and morphological quenching mechanisms.