This 2-phase study will determine the safety of treating patients with non-small cell lung cancer with the genetically engineered HyperAcute-Lung cancer vaccine. It will establish the proper vaccine dose and will examine side effects and potential benefits of the treatment. The vaccine contains killed lung cancer cells containing a mouse gene that causes the production of a foreign pattern of protein-sugars on the cell surface. It is hoped that the immune response to the foreign substance will stimulate the immune system to attack the patient's own cancer cells that have similar proteins without this sugar pattern, causing the tumor to remain stable or shrink.