The primary drivers of yeast endocytosis are actin polymerization and curvature-generating proteins, such as clathrin and BAR domain proteins. Previous work has indicated that these factors may not be capable of generating the forces necessary to overcome turgor pressure. Thus local reduction of the turgor pressure, via localized accumulation or activation of solute channels, might facilitate endocytosis. The possible reduction in turgor pressure was calculated numerically, by solving the diffusion equation through a Legendre polynomial expansion. It was found that for a region of increased permeability having radius 45 nm, as few as 60 channels with a spacing of 10 nm could locally decrease the turgor pressure by 50%. We identified a key dimensionless parameter, p = P1a/D, where P1 is the increased permeability, a is the radius of the permeable region, and D is the solute diffusion coefficient. When p > 0.44, the turgor pressure is locally reduced by >50%. An approximate analytic theory was used to generate explicit formulas for the turgor pressure reduction in terms of key parameters. These findings may also be relevant to plants, where the mechanisms that allow endocytosis to proceed despite high turgor pressure are largely unknown.