The bacterial cell wall is a network of sugar strands crosslinked by peptides that serve as the primary structure for bearing osmotic stress. Despite its importance in cellular survival, the robustness of the cell wall to network defects has been relatively unexplored. Treatment of the gram-negative bacterium Escherichia coli with the antibiotic vancomycin, which disrupts the crosslinking of new material during growth, leads to the development of pronounced bulges and eventually of cell lysis. Here, we model the mechanics of the bulging of the cytoplasmic membrane through pores in the cell wall. We find that the membrane undergoes a transition between a nearly flat state and a spherical bulge at a critical pore radius of ~20 nm. This critical pore size is large compared to the typical distance between neighboring peptides and glycan strands, and hence pore size acts as a constraint on network integrity. We also discuss the general implications of our model to membrane deformations in eukaryotic blebbing and vesiculation in red blood cells.