Republican U.S. presidential contender Herman Cain pushed ahead with his struggling campaign on Wednesday, saying he would not be deterred by allegations of an extramarital affair.

At a campaign stop in Ohio, Cain said his supporters were sticking with him despite the latest charges and accused his critics of trying to bring down his upstart White House bid.

They are attacking my character, my reputation, and my name, in order to try and bring me down, Cain said of his unnamed critics. But you see I don't believe that America is going to let that happen.

Cain, 65, denies he had an affair with Atlanta businesswoman Ginger White, who claims their 13-year, on-and-off relationship began in the mid-1990s. But he says he is reassessing the viability of his campaign.

We are reassessing as we speak, Cain said.

Cain, a former pizza company executive and lobbyist who led the Republican White House race barely more than a month ago, has nosedived in polls after a series of sexual harassment charges and campaign missteps.

In West Chester, a Cincinnati suburb that was the first event on a three-stop Ohio tour, Cain tried to focus on his remedies for an ailing economy and ignored questions about how long his reassessment would take.

There is a groundswell of support, he told reporters of the reaction to White's claims. So far the new disclosures have not sparked widespread defections, although two state representatives in New Hampshire backed off their support.

Some of those in Ohio who came out to hear Cain speak said they were willing to give the candidate a chance.

I am more convinced than I ever was. I believed him and I am going to donate to him and vote for him, said Christine Bolte, 46, a substitute teacher who is working as a cashier at Wal-Mart to help pay her bills.

The allegation of an affair came just five weeks before Iowa kicks off the Republican battle for the right to challenge Democratic President Barack Obama, giving Cain little time to resurrect his once high-flying campaign.

White told ABC's Good Morning America program that she remained in contact with Cain until last week.

I've received gifts and money for the last 2 1/2 years, consistently, White said, adding Cain also took her on several trips. But she said he sought nothing in return.

This was not sex for cash, White said.

ABC said White's phone records for October and November show numerous text exchanges with Cain, including daily contact in early November as reports emerged of sexual harassment allegations from other women.

Just up until last week, that was my last contact with Mr. Cain, said White, 46. She did not disclose what was discussed in the text exchanges but said Cain did not try to stop her from speaking out.

The allegations could be the end of the political line for Cain, who also has been hit by sexual harassment allegations from four women and stumbled on the campaign trail. He raised alarm among conservatives with confusing comments about abortion and badly fumbled a question on Libya policy.

(Additional reporting by David Morgan; writing by John Whitesides; editing by Mohammad Zargham)