Cells rely on cytokines to coordinate their activation, differentiation, proliferation and survival. In particular, γC cytokines (interleukins IL-2, 4, 7, 9, 15, and 21) regulate the fate of leukocytes. The signaling cascade induced by these cytokines is relatively simple, and involves the phosphorylation of receptor-associated Janus-like kinases (JAK). Here, we explore the cell-to-cell variability of cytokine responses in primary mouse T~cells, and find a paradoxical and quantitative imprint of receptor expression levels and other signaling components. For instance, high abundance of the common $\gamma_c$ chain reduces cytokine responses (both in terms of signaling amplitudes and characteristic cytokine concentrations triggering 50% of the response). We develop mathematical models to quantify how limited abundances of signaling components (e.g. JAK or other cytokine receptor subunit chains) may explain our experimental observations. We conclude by generalizing this observation of cell-to-cell signaling variability to other ligand-receptor-kinase systems.