An ethics complaint filed against the Arlington mayor accuses him of asking the only minority City Council member whether he was attending a conference for "a bunch of Mexicans."
According to the complaint, Cluck made the comment Feb. 7 in Councilman Robert Rivera's office.
Cluck said he recalls asking Rivera whether he was attending a Latino event at a Mexican restaurant.
Rivera told the mayor he was attending the National Association of Latino Elected and Appointed Officials leadership conference in Washington, D.C. The complaint alleges Cluck said, "Oh, a bunch of Mexicans?"
Cluck responded to the complaint on Sunday. He said he doesn't recall using those words. Cluck said he is "totally colorblind" and said that he "sincerely apologizes" if anything he said offended anyone.
"There's nothing wrong with the word 'Mexican,'" Arlington resident Patricia Vaughn said. "You can say something like, you know, 'a group of Mexicans' if that's what they are. But it could all be in your tone or how you use the term."
"I would have rather him used the word Hispanic or Latino instead of just the word Mexican, but it all depends on how you use it," said Iolaire Sino, another resident.
Veronica Rincon, who is half Mexican, said she thinks some people are too sensitive. But she also said the using the term "Mexican" when it doesn't apply is what most often offends people.
"There are a lot of Spanish people that if you call them Mexican, they get real offended, and they're like, 'No we're Puerto Rican,' or, 'We're Cuban,' and they take real pride in where they're from," she said.
NBC 5's Mola Lenghi contributed to this report.