"Given everything that has gone on, it's obviously something he considered, but he's determined to serve out his term," Joel Sawyer, Sanford's communication director told ABC News.
Meanwhile, at least one member of Sanford's own party is calling for a criminal investigation into whether he broke the law by not informing his lieutenant governor -- who would be in charge in case of emergency -- of his departure and using state money to finance his trips to see his mistress. The governor's chief rival, Republican state Sen. Jake Knotts, told ABC News Sunday that he will pursue a criminal prosecution, even if he has to go to Washington, D.C.
Knotts last week asked South Carolina prosecutors to launch a criminal probe and said that he plans to pursue an investigation in the state legislature and the state attorney general's office. If the state authorities don't respond, Knotts said he is ready to go to the nation's capital and seek a federal probe.
"When you can't get results in your own state, there is a Justice Department in Washington," Knotts told ABC News. "I don't want to go that route. I want us to wash our own laundry and clean up our own act."
"Somebody's gonna look at this," Knotts said. "Somebody's gonna look to the bottom of it, and somebody's gonna give me some answers."
Knotts and some others accuse the governor of leaving the state to visit his companion without turning over control and charging taxpayers for an earlier stop in Argentina where he visited her. Sanford said last week he'll repay more than $8,000 for that stop, which he claimed was strictly a trade trip set up by state commerce officials.
"At this point we have not launched an investigation," Reggie Lloyd, director of the South Carolina Law Enforcement Division, told ABC News Sunday. "We don't anticipate it unless somebody brought us new facts."
Knotts is a longtime Sanford critic, but he insists that he is not in the running for next year's gubernatorial race, for which Lt. Gov. Andre Bauer and Attorney General Henry McMaster are seen as frontrunners.
The South Carolina legislature, which can call for an investigation, is not in session until January. It can be called into a special session, but staffers said there has so far been little talk about that. In the legislature's absence, the attorney general can call a probe, but some say that's unlikely.
Bauer told The Associated Press last week that Sanford should stay in office but admitted that he would have an advantage in the election if Sanford resigned.
"He was going to be a lame duck as it was, and now there's a possibility he could be the lamest lame duck we've ever had in South Carolina," said Warren Bolton, associate editor of The State.
Sanford continued to insist Monday that he intends to remain in office for the remaining 18 months of his term.
Even though he initially considered resigning, Sanford told The Associated Press that he spoke with close spiritual and political associates who advised him to fight to restore the public's and his family's trust in him.
"Resigning would be the easiest thing to do," he said, but added that he won't quit and has to "go through that voyage over the next 18 months."
The governor's wife has said whether he resigns or not is up to him and she is only focused on rebuilding the family.