Three-dimensional supranucleosomal chromatin packing plays a profound role in modulating gene expression by regulating transcription reactions through mechanisms such as gene accessibility, binding affinities, and molecular diffusion. Here, we use a computational model that integrates disordered chromatin packing (CP) with local macromolecular crowding (MC) to study how physical factors, including chromatin density, the scaling of chromatin packing, and the size of chromatin packing domains, influence gene expression. We computationally and experimentally identify a major role of these physical factors, specifically chromatin packing scaling, in regulating phenotypic plasticity, determining responsiveness to external stressors by influencing both intercellular transcriptional malleability and heterogeneity. Applying CPMC model predictions to transcriptional data from cancer patients, we identify an inverse relationship between patient survival and phenotypic plasticity of tumor cells.