Phase II trial to study the effectiveness of combining oblimersen with imatinib mesylate in treating patients who have chronic myelogenous leukemia that has not responded to previous treatment with imatinib mesylate. Imatinib mesylate may stop the growth of cancer cells by blocking the enzymes necessary for cancer cell growth. Oblimersen may help imatinib mesylate kill more cancer cells by making cancer cells more sensitive to the drug.