There is a need for more treatment options for patients with recurrent squamous cell cancer of the head and neck (SCCHN). These tumors usually have a variety of genetic defects that include disruption of the p53 pathway, a pathway that would ordinarily work to prevent the development of tumors. In this study the transfer of the p53 gene to tumor cells using a modified adenovirus (INGN 201) will be compared to methotrexate in patients who have failed surgery, radiotherapy and chemotherapy with platinum or taxanes.