Sanford went out of his way to apologize to Davis at Wednesday's mea culpa news conference, in which he admitted to cheating on his wife with a woman named Maria.
The confession came after Sanford was caught returning from a five-day trip to Argentina, during which his staff claimed he was hiking in the Appalachian mountains.
Davis said he was "tremendously surprised" by the admission in an interview with Early Show co-anchor Harry Smith on The Early Show Thursday.
As Sanford awaits the political fallout, Davis said he thinks the governor can weather the storm, saying South Carolinians had a "tremendous capacity for forgiveness."
"Now, I think the South Carolina people also have a fine nose for hypocrisy," Davis told Smith. "So the next few days are going to tell the tale about whether or not Gov. Sanford is sincere in terms of taking responsibility for his actions, and the pain he's caused the people."
"And knowing the man that he is, I think he will make that case, and I think the South Carolina people will give him a chance."
When pressed by Smith on whether Sanford's support for President Bill Clinton's impeachment in 1998 following an affair with White House intern Monica Lewinsky, Davis said that "as reprehensible as Gov. Sanford's actions were … let's remember the grounds for impeachment for President Clinton was for lying under oath."
"We're all human," Davis said. "We all have failings."