"In my career, I've made it a point that I don't talk about people's personal problems," Barbour said. "The people of South Carolina have got to decide, and he's got to decide, if he'll ever run for anything."
Asked directly if Sanford should resign, Barbour said: "I don't think he should."
When Barbour took over leadership of the Republican Governors Association after Sanford resigned this week, he already had back-to-back trips scheduled to the early presidential voting states of Iowa and New Hampshire.
Sanford admitted Wednesday that he has been having an extramarital affair, and he kept his whereabouts secret while he traveled to Argentina. The matter came only days after Republican Nevada Sen. John Ensign admitted to an extramarital affair.
Barbour, speaking during a taping of the Iowa Public Television program, "Iowa Press," dismissed the political impact of Sanford's situation on Republicans in future elections.
"I don't think there will be any effect, literally," said Barbour. "I don't think it's going to change how one person is going to vote."
Asked if Sanford faces trouble because he misled others about his whereabouts, Barbour was dismissive.
"I don't know what he said differently, and he didn't say anything to me, so I'm not going to prejudge that," said Barbour. "The Sanfords have got something they've got to work through and I think they're trying to work through it."
He said the family is likely focused more on their personal problems than the governor's political future.
"What that means politically right now for them is probably a whole lot less important than what it means for the family," he said.
He conceded the scandals have been distracting.
"It's better for Republicans when campaigns are about public policy and ideas - there's no question about that," Barbour said.
But he insisted that key governors' races in Virginia and New Jersey have not gotten off message because of the enormous attention Sanford is getting.
"I've spent the last few days in Virginia and New Jersey," said Barbour, a former head of the Republican National Committee. "What they are talking about are governors' races in Virginia and New Jersey.'
As leader of the Republican Governors Association, Barbour said he's focused on the business of electing Republicans.
"We are trying to focus on what is the business at hand," he said.
Barbour was in Iowa to talk to Republican activists about how to rebuild a state party that's suffered historic defeats in the last couple of elections. The governor has been mentioned as a possible 2012 presidential candidate, and his trip to the state that holds the first presidential caucuses has prompted speculation about his plans. Term limits block him from seeking re-election as governor.
"I talk to them about party-building. I don't know what presidential candidates coming out here talk about," Barbour said.
On Wednesday, he was in New Hampshire, home of the first primary in the nominating season.
But Barbour insisted he was focusing on governors' races this year, and the midterm election next year.
After the midterm election, he said, he will have plenty of time to consider a run for president, something he insisted was a long-shot idea.
"If, after that, it seems like a reasonable thing, I'll consider it," he said. "I would be very surprised if I turned out to be a candidate for president, and my wife would be even more surprised."