During a press conference Wednesday, Sanford said that his eight-year friendship with the mystery woman transformed into a romance about a year ago and that he had seen her three times since the "whole sparking thing."
Though Sanford's multiple trips to Buenos Aires have some crying foul, South Carolina Democrats don't foresee an investigation.
"He is surrounded by ... a total Republican administration," Rutherford said. "Republicans seem, at this point, to be coalescing behind him."
The South Carolina state Legislature does not convene until January. It can be called into a special session before then, but Rutherford said that is unlikely to happen. A Senate staffer told ABCNews.com there has been no discussion of an investigation or impeachment in the state Senate.
In the legislature's absence, the attorney general can call for an investigation. The attorney general's office did not return calls to ABC News seeking comment.
ABC News' chief Washington correspondent George Stephanopoulos noted today on "Good Morning America" that Republican politicians have generally fared better than their Democratic counterparts after sex scandals.
While Sanford and Sen. John Ensign, R-Nev., who admitted an affair earlier this month, show no signs of resigning their posts, former New York Gov. Eliot Spitzer left his job after winning a landslide election when he got caught in a prostitution scandal. And former New Jersey Gov. Jim McGreevey also resigned after he admitted to an affair with a male staff member.
Rutherford said that if a Democrat were involved in such a scandal in Republican-heavy South Carolina, the situation would be very different.
"These are the same people who jumped on Bill Clinton, and now they're saying, 'let's talk about forgiveness, let's talk about family,'" he said.
Stephanopoulos said Sanford's admission was unprecedented, in part, because of how candid he was about his infidelity.
"We've never seen anything like this ... the raw emotion, the amount of information the governor gave out was simply incredible," Stephanopoulos said.
Sanford's former chief of staff said he was just as blindsided by his friend's announcement as the public.
"What I saw yesterday ... is a man who realized he sinned," Tom Davis told "GMA" today, but he added that Sanford "should not resign."
Sanford invoked Davis' name several times while admitting to the affair during Wednesday's press conference, emphasizing how he "let down the Tom Davises of the world."
Davis, a close family friend who lived in the family's basement for six months during Sanford's first race for governor in 2002, said that Sanford did let him down.
"I think I represent to him people that have believed in him, people that have believed in the powers of his ideas," Davis said.
Davis said he spoke with Sanford for about an hour-and-a-half before the press conference. Up until that point, Davis said he had no idea that the governor's trip would blow up into such a wide-reaching scandal.
Davis said that while he has not spoken to the governor's wife, Jenny Sanford, he believes his friend understands "the very real hurt he knows he caused people."