Mr. Romero could not be reached for comment. Mr. Gorzkowski, a naturalized United States citizen who operates a deli in North Carolina, said the video was extremely embarrassing, especially after a Polish newspaper ran an article suggesting that he was at the center of a voting scandal in the United States.

‘Never Had Any Problem’

Late last month, Ms. Engelbrecht was in Columbus, Ohio, for a True the Vote workshop. About 90 people signed up for the event at a suburban Holiday Inn, where they listened to speeches and discussed how to challenge questionable voters, including 51,000 “nonexistent” people in just one county that True the Vote’s Ohio volunteers say are registered to vote.

During the meeting, Anita MonCrief, True the Vote’s senior adviser, unleashed her vitriol at what she said was a coalition of voter registration groups, accusing them of “doing voter fraud since at least the early ’90s,” she said.

“And these groups target minority areas. Why? Because it’s so much easier to go work in those areas where they say people have been forgotten or they don’t have a voice. Then, when anybody pays a little bit of attention to the fact that there’s a high level of fraud coming out of the African-American communities, they say: ‘Oh, you’re a racist. You don’t want black people to vote,’ ” said Ms. MonCrief, who is black. “Vote fraud deniers is what I call them.”

After the event, the volunteers, known as the Ohio Voter Integrity Project, submitted challenges of 380 registered voters in Hamilton County, which includes Cincinnati. One of the voters, Teresa Sharp, received a notice from her local Board of Elections stating that her family’s right to vote had been challenged and ordering her to attend a hearing on Sept. 10.

“I’ve always voted,” said Ms. Sharp, who had even been a poll worker. “Never had any problem.”

At the hearing, she said she asked, “Why are you all harassing me?” She said she believed it was because “either they don’t want Obama in there or the fact that I’m black.”

Amy Searcy, the director of the Hamilton County Board of Elections, said there was no discernible racial pattern in the challenges. Of the 380 challenges, about 35 voters will have to prove that their addresses are current if they appear at the polls. A vast majority of the objections were thrown out.

In the case of Ms. Sharp, a representative of the Ohio Voter Integrity Project withdrew the challenge and apologized to the family.