We present a kpc-scale analysis of the relationship between the molecular depletion time (τ^mol_dep) and the orbital time (τorb) across the field of 39 face-on local galaxies, selected from the EDGE-CALIFA sample. We find that, on average, 5 per cent of the available molecular gas is converted into stars per orbital time, or τ^mol_dep˜ 20 τ_orb. The resolved relation shows a scatter of ˜0.5 dex. The scatter is ascribable to galaxies of different morphologies that follow different τ^mol_dep-τorb relations which decrease in steepness from early- to late types. The morphologies appear to be linked with the star formation rate surface density, the molecular depletion time, and the orbital time, but they do not correlate with the molecular gas content of the galaxies in our sample. We speculate that in our molecular gas rich, early-type galaxies, the morphological quenching (in particular the disc stabilization via shear), rather than the absence of molecular gas, is the main factor responsible for their current inefficient star formation.