NEW YORK -- Illinois Republican U.S. Senate candidate Alan Keyes is causing a stir at the party's national convention in New York City -- and among Illinois Republicans.

According to the Chicago Tribune, when Keyes told two interviewers on Sirius OutQ, a New York-based satellite station that provides 24-hour gay and lesbian programming, that homosexuality is "selfish hedonism," his hosts asked if Mary Cheney, daughter of Vice President Dick Cheney is a "selfish hedonist." "Of course she is," Keyes said, according to the paper. "That goes by definition."

NBC5 reported on Wednesday that some of the biggest names in Illinois Republican politics said Keyes' views were offensive. The controversy flared with Vice President Dick Cheney, who was preparing to speak to the convention on Wednesday night.

Illinois State Rep. Tom Cross, who is the House minority leader, said candidates have a right to articulate a position, but should not personalize their feelings.

"When you start to talk about an individual, especially someone's daughter, and personalize it, you're going into territory that a lot of people find offensive," he said. "Stating your position is one thing -- personalizing it is probably not the right way to handle it. It's not something I would have done."

Keyes defended his remarks, saying that if his daughter were a lesbian, he would tell her she was committing a sin and should pray. The interview with OutQ centered on Keyes' opposition to same-sex marriage. Keyes also said in the interview that family is defined by having children, according to the Tribune.

At the Illinois caucus on Wednesday, he did not back down from his comments about homosexuality.

"We should look [homosexuality] right in the eye," Keyes said. "It is a self-centered, selfish, self-oriented pursuit of pleasure. If my own daughter were a homosexual or a lesbian, I would love my daughter but I would tell my daughter that she was in sin."

Former Gov. Jim Thompson was very harsh in his criticism of Keyes, Kay reported.

"I think the people of Illinois would find those kinds of remarks offensive and I think it's an offense to the political process that we have to suffer a candidate on our ticket who says things like that," Thompson said. "So it is not something that I as a voter would put up with, and I don't think the people of Illinois will put up with it, either."

Republican Illinois Congresswoman Judy Biggert, an abortion-rights Republican, was equally offended.

"I think it is shameful -- I really do," she said. "I think he should apologize. This is destroying everything that we've been building."

Former Gov. Jim Edgar chairs the president's re-election campaign in Illinois.

"It is an unfortunate thing. I think it takes away from the real issues in this campaign."

Illinois Party Chairman Judy Baar Topinka minced no words.

"You don't attack other people's children," she said. "I can't stand behind that kind of an idiotic comment -- that is exactly what it is, idiotic. If somebody went after my son, you know I would go for the jugular. You just don't do that."

A Bush/Cheney spokesman said Keyes remarks were inappropriate. In Pennsylvania, Arizona Sen. John McCain, who is a Republican, said, "I think it's clear we lose Illinois."

Alan Keyes also walked off the convention floor Tuesday night when California Gov. Arnold Schwarzenegger spoke. Keyes said on Wednesday that he didn't have time to explain why, but there are reports in the New York media he did it because Schwarzenegger supports abortion rights.

Rick Garcia, director of Equality Illinois, a non-partisan gay rights group, said Keyes' views are not representative of either Illinois Republicans or Democrats, according to the Tribune.

Keyes is running against Democratic U.S. Senate candidate Barack Obama.