Sanford and Colbert Busch are competing to fill the House seat vacated by former Rep. Tim Scott (R) when he was appointed to the Senate.
Sanford's campaign has been struggling amid legal problems and polling that shows him falling behind in the special House election. Candidates typically don't demand more debates, or stage political stunts for media attention, when they are the front-runner.
Her campaign fired back against Sanford on Wednesday:
"While Mark Sanford continues his desperate campaign to deceive voters, Elizabeth Colbert Busch is spending her time with real people who support her campaign," said spokesman James Smith, who said the Democrat was meeting with a group of Republican supporters on Wednesday.
"She doesn’t have to resort to phony cardboard cutouts to talk with the people of South Carolina."
Sanford trailed Colbert Busch by 9 points in a recent survey from the Democratic-affiliated Public Policy Polling, and he has had to deal with continuing questions about his ex-wife's charges that he repeatedly trespassed at her home.
The National Republican Congressional Committee
has said it won't give him any more support this election.