Among the most closely watched Democratic women this year are Diane Farrell , challenging Representative Christopher Shays in Connecticut ; Gabrielle Giffords and Patty Weiss , vying for the Democratic nomination for an open seat representing the Tucson area ; Patricia Madrid , the New Mexico attorney general challenging Representative Heather A. Wilson ; Ms. Duckworth , the Iraqi war veteran , seeking the open seat outside Chicago ; Francine Busby , running for the California seat left vacant by the bribery conviction of former Representative Randy Cunningham , and Ms. Murphy , challenging Mr. Gerlach in Pennsylvania .