Herman Cain told Fox News on Wednesday he is consulting with his family on whether to stay in the presidential race and plans to make a decision within a week, as he continued to defend himself against allegations of a 13-year extramarital affair. 

The Republican presidential candidate lashed out at his critics, saying he's the victim of a "direct character assassination" and that he doesn't understand where the latest allegations are coming from. 

After hosting three rallies Wednesday in the general election battleground state of Ohio, Cain said supporters have been "overwhelming" in encouraging him to stay in the race. But he said the constant media coverage of the allegations, including earlier sexual harassment allegations, has weighed on his family. 

"I've got to think about my family first," Cain said. "That is absolutely my No. 1 priority."

He said the allegations are taking an "emotional toll" on his wife, Gloria. "It has had a very damaging effect on her emotionally," Cain said, adding that he's explained everything to his wife. 

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"My wife loves me," Cain stressed. 

The candidate has denied the latest allegations after Ginger White, an Atlanta businesswoman, claimed in media interviews that she and Cain had a long-running sexual affair. 

Cain told Fox News the claim came "totally out of the blue." 

He said White was just somebody he was helping financially, and that it wasn't unusual for him to do that. "I was in business for over 40 years. I have worked with and helped a lot of people, male and female," Cain said. 

He described the charges as part of a character assassination campaign, though he conceded he doesn't know who might be behind it. 

"I can only conjecture that maybe I am the Democrats' worst nightmare if I win the nomination," Cain said, later suggesting that some Democrats may want former House Speaker Newt Gingrich to win the nomination so they can go after his personal life. 

Cain said he expects to make a decision within "several days," after consulting first his family and then taking the pulse of his supporters and donors. 

"A week from now, I will have made a final decision," he said. 

White steadfastly stood by her assertion in an interview Wednesday on ABC's "Good Morning America" and said she was "disappointed" by Cain's characterization of her. She called her relationship with Cain "a very casual affair" that lasted more than a dozen years. 

"I'm not here to say anything negative about Mr. Cain," White said, although White added that she didn't think he should be president. 

She elaborated on her claims, saying she took several trips with Cain, including a flight to Las Vegas to see a Mike Tyson-Evander Holyfield boxing match. She also said she had "consistently" received gifts and money from Cain over the past two and a half years, but said it was "not sex for cash." 

Following Monday's developments, some Cain supporters have started to defect. 

In Iowa, Cain's campaign has lost some precinct-level supporters following the new allegations, according to Steve Grubbs, Cain's Iowa chairman. Cain was in Iowa for a day last week to film a new ad, but aides say that spending to air it was on hold pending the fundraising in the days to come. 

Still, some are sticking by him. 

Florida state Rep. Scott Plakon, one of four chairmen for Cain's Florida campaign, said he wanted to see more evidence. 

"If it is true that he didn't do this, I think he should fight and kick and scratch and win," Plakon said. 

But if Cain did have the affair, Plakon said, "that would be very problematic," he said. "There's the affair itself and then there's the truthful factor. He's been so outspoken in these denials." 

Questions about the campaign's viability hovered over Cain's one-day bus tour through Ohio. 

But Cain received a standing ovation after he spoke about what a "Cain administration" would do at one stop. And he said that while some people predicted that the room would be empty, "I don't see any empty seats." 

"It's been a groundswell of positive support," Cain insisted to reporters later. 

Cain's latest turmoil comes just five weeks before the first votes are cast in the state-by-state march to the nomination. 

White's revelation was the latest setback for a candidate who has been under scrutiny in the past month, since it was revealed that the National Restaurant Association paid settlements to two women who claimed Cain sexually harassed them while he was president of the organization. A third woman told The Associated Press that Cain made inappropriate sexual advanced toward her but that she didn't file a complaint. A fourth woman also stepped forward to accuse Cain of groping her in a car in 1997. 

Cain has denied wrongdoing in all cases. 

The Associated Press contributed to this report.