Synthetic gene circuits perturb the physiology of their cellular host. The extra load on endogenous processes shifts the equilibrium of resource allocation in the host, leading to slow growth and reduced biosynthesis. Here we built integrated host-circuit models to quantify growth defects caused by synthetic gene circuits. Simulations reveal a complex relation between circuit output and cellular capacity for gene expression. For weak induction of heterologous genes, protein output can be increased at the expense of growth defects. Yet for stronger induction, cellular capacity reaches a tipping point, beyond which both gene expression and growth rate drop sharply. Extensive simulations across various growth conditions and large regions of the design space suggest that the critical capacity is a result of ribosomal scarcity. We studied the impact of growth defects on various gene circuits and transcriptional logic gates, which highlights the extent to which cellular burden can limit, shape, and even break down circuit function. Our approach offers a comprehensive framework to assess the impact of host-circuit interactions in silico, with wide-ranging implications for the design and optimization of bacterial gene circuits.