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. We developed a feedback intereference mechanism that can explain delays and transitions to aggressive stages in chronic cancers. Here, we apply this model to the specific case of CML where specific mutations found from microarray experiments cause hypersensitivity to Wnt signaling in cancerous GMPs. Furthermore, the combination of elevated cell growth and Wnt signaling create a positive feedback leading to characteristic switch-like dynamics. This allows for a long period of mild cancerous cell growth followed by a strong and sharp switch to extreme cancerous cell growth. We propose that this mechanism explains the existence of a clinically distinguishable but a genetically indistinguishable stage in CML. This also reinforces recent findings that indomethacin, an NSAID that inhibits Wnt signaling, is an effective treatment of CML. Our study may predict novel treatment strategies for patients in accelerated and blast crisis phase where current treatments are largely ineffective.