Sanford disappeared for nearly a week to Argentina without informing his family, staff, security detail or Bauer, who is in charge should emergency decisions need to be made in the governor's absence.
Many who have called for Sanford to resign raised two questions: Did the governor use money from state coffers to finance his private escapades, and did he break the law by not informing the lieutenant governor?
Despite the discussion surrounding personal political interests, some Republicans have strong words for Sanford.
After a meeting of GOP leaders Thursday at the state capital, state Sen. Jake Knotts called for the governor's resignation and a criminal investigation into his travels.
"He should strongly consider resigning for the good of the taxpayers of South Carolina, and the good of this state," said Knotts.
The governor "talked about how our leaders have stepped away from our core values, and said one thing on the campaign trail or out in the public and did something different in the background," said Glenn McCall, a local representative to the Republican National Committee Thursday, adding that he should resign "for the sake of the party."
Former South Carolina GOP Chairman Katon Dawson said state Republican officials will want to make sure everything is out in the open.
"I would say that our elected Republican officials are going to want as much disinfectant on this process as they can get," said Dawson.
Former presidential hopeful and ex-Arkansas Gov. Mike Huckabee said Thursday Sanford should spare himself and his family public scrutiny by stepping down, "not because of his personal behavior, but for putting his personal behavior above the responsibility for being available to govern and lead in the event of a crisis."
While some Democrats, like Rutherford, have called for the Sanford's resignation, others feel Sanford's unstable political future bodes ill for Republicans and may boost Democrats' chances in the next gubernatorial election.
Not only is Sanford the second GOP member to admit an extramarital affair this month -- Sen. John Ensign, R-Nev., being the first -- he was also on the forefront in denouncing President Bill Clinton for his affair with Monica Lewinsky.
"What the American public cares about is the issues of integrity and the issue of trust, because if they don't trust their lawmaker, they won't trust the laws that the lawmakers create," Sanford said in 1997, blasting Clinton on "Good Morning America" during his impeachment scandal.
Sanford, who has been known to invoke religious rhetoric and the Bible in political matters, resigned from his post as chairman of Republican Governors Association after announcing his affair.
ABC News' chief Washington correspondent George Stephanopoulos notes that Republican politicians have generally fared better than their Democratic counterparts after sex scandals.
While Sanford and Ensign 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.