This study is designed to assess the safety and preliminary efficacy of five different doses of DTA-H19 given as six intravesical infusions into the bladder of patients with superficial bladder cancer [stages Ta and carcinoma in situ (CIS)] who have failed intravesical therapy with Bacille Calmette-Guérin (BCG). The primary safety outcome measure is the maximum tolerated dose (MTD). DTA-H19 is a DNA plasmid that contains H19 gene regulatory sequences that drive the expression of an intracellular toxin [diphtheria toxin A (DTA) chain]. This is a Patient-Oriented, Targeted Therapy as DTA expression is triggered by the presence of H19 transcription factors found only in bladder tumor and not normal bladder cells.