In many cancers, such as Chronic Myelogenous Leukemia (CML), pancreatic, and colorectal cancer, long delays exist between the initiation of the disease and the onset of debilitating symptoms. The early stages of these diseases present manageable symptoms and, in the case of CML, highly effective treatment options. Progression to the more aggressive stages of the diseases limits effective treatment and significantly exacerbates patient prognosis. The mechanisms causing delay and disease progression are largely unknown. The later stages of these diseases are characterized by excessive build up of primitive cell types, indicating a disruption in the normal cell differentiation process that is commonly regulated through feedback from differentiated types. In this study, we propose a mechanism where mutated primitive cells produce a feedback interference signal that desensitizes them to a normal homeostatic feedback. Using a mathematical model, we show that this mechanism can account for the long delay period between occurrence of genetic changes and symptomatic onset characterized by fast growth of cancerous cell population. Finally, we explore novel concepts for potential treatment of chronic cancers.