ABC News’ Teddy Davis reports: Sen. John McCain, R-Ariz., is jabbing GOP Senate rival J.D. Hayworth for not severing his ties to ALIPAC, a conservative anti-illegal immigration group whose president issued a press release on Tuesday alleging that Sen. Lindsey Graham, R-S.C., is gay and that his homosexuality is being used to blackmail him into cooperating with Democrats on comprehensive immigration reform. Graham’s office declined to respond directly to ALIPAC on Tuesday and Wednesday. Instead, a Graham spokesman is referring news organizations to a 2006 story in GQ magazine and a 2001 story in The State newspaper in which Graham, who is single, indicated that he is not gay and that he would like to one day find a wife and have children. “It’s unfortunate that Congressman Hayworth’s fetish with the extreme fringe continues,” said McCain spokesman Brian Rogers in a statement provided to ABC News. “Is Congressman Hayworth really so desperate to show any support for his candidacy that he would continue to embrace the support of a group that’s been linked to white supremacists, neo-Nazis and anti-Semites — even after his spokesman ‘strongly repudiated’ ALIPAC’s President?” “From his close embrace of Mr. Gheen and ALIPAC, to peddling conspiracy theories about the President’s birth certificate and man-horse marriage, Congressman Hayworth has made clear that he feels most comfortable on the extreme fringe,” Rogers continued. “While Congressman Hayworth courts extreme elements, Senator McCain is proud to have the support of Arizona leaders on the front lines fighting to secure our border, including Cochise County Sheriff Larry Dever and Pinal County Sheriff Paul Babeu.” McCain’s spokesman made his statement about Hayworth’s “fetish with the extreme fringe” continuing after Hayworth declined to repudiate the support of ALIPAC on Wednesday. “We strongly repudiate these comments but we do welcome the support of all Arizona voters who want to fix this current crisis in illegal immigration,” said Hayworth communications director Mark Sanders. Asked why Hayworth is not repudiating the group’s endorsement, Sanders said: “ALIPAC and its members are people who are strongly behind and in favor of addressing this illegal alien crisis.” To back up its charge about white supremacists, neo-Nazis, and anti-Semites, the McCain campaign is pointing to a May 26, 2009, article by the Anti-Defamation League. Today is not the first time that the McCain campaign has sought to paint Hayworth as an extremist. Earlier this month, the McCain campaign released a web video mocking Hayworth as someone who is obsessed with exposing Obama’s “secret Kenyan birthplace.” Watch it HERE. The gay-baiting attack on Graham is the latest sign of just how heated the immigration debate has become. The headline of ALIPAC’s Tuesday press release called on Graham to “admit his homosexuality.” The press release was accompanied by video of William Gheen, ALIPAC’s president, making the gay-baiting charge during a Tea Party rally which took place on Saturday, April 17, in Greenville, S.C. “Come out of that closet, Lindsey. Come out of that log cabin closet. Barney Frank is more honest and brave than you because at least we know about Barney Frank, and nobody’s going to hold it over his head,” said William Gheen, the president of Americans for Legal Immigration PAC (ALIPAC). “. . . I don’t care about your private life, Lindsey, but as our U.S. senator, I need to figure out why you’re trying to sell out your own countrymen, and I need to make sure you being gay isn’t it.” Watch Gheen’s attack on Graham HERE starting at 7:10. Graham is a target because he is cooperating with Sen. Chuck Schumer, D-N.Y., on comprehensive immigration reform legislation.