Herman Cain will not end his presidential campaign in response to the allegation that he had a 13-year extramarital affair, he said in a defiant speech in Dayton, Ohio, on Wednesday.

The American people are going to raise some Cain in 2012, he told a cheering audience of several hundred supporters. They want you to believe that we can't do this. They want you to believe that with enough character assassination on me, I will drop out. Well, the American people have a different idea.

It is unclear whether the American people have as much faith in Cain as he portrays. In late October, he had 30 percent support in a Quinnipiac poll. This month, after a series of allegations that he sexually harassed National Restaurant Association employees in the 1990s, he has just 14 percent in the same poll -- and that was before Ginger White came forward with her claim of a 13-year affair.

Cain is planning to hold a press conference in Manchester, N.H., at 8 p.m. on Wednesday, and his New Hampshire field director, Charlie Spano, told The Boston Herald that Cain was still in it to win it.

We've reached out to as many volunteers as possible, and they can meet Mr. Cain and reconnect, Spano said. More people have expressed support for Mr. Cain in the last few days than ever before.

This was an odd statement given that Cain is polling in the single digits in New Hampshire, down from a high of 24 percent in mid-October.

That's not to say that Cain doesn't still have his supporters. It was clear from his appearance in Ohio that there are many voters who will stick with him regardless of what allegations come out.

Look, a lot of people in office haven't had the most squeaky clean morals -- not that I'm saying there's any truth to what's been out there, one voter, Steve Fields, 48, told The New York Times. We're looking for someone different to lead this country, and I think he's the one to do it.

But it is equally clear from the polls that the number of such voters is limited, and Cain's prospects of winning the nomination seem slimmer every day.