Republican John McCain (news, bio, voting record) accused presidential rival Mitt Romney of flip-flopping on immigration Monday and said with sarcasm: "Maybe his solution will be to get out his small varmint gun and drive those Guatemalans off his lawn." McCain also said he was disappointed in potential candidate Fred Thompson for opposing immigration legislation the Arizona senator is co-sponsoring. The immigration spat comes as the GOP race turns increasingly contentious and as Romney, the former Massachusetts governor, shows signs of gaining steam in Iowa and New Hampshire while Thompson lays the groundwork for what increasingly appears to be his own White House bid. After months of behind-the-scenes aggression between the McCain and Romney campaigns, the two rivals openly sparred last week during a debate at the University of South Carolina. In a conference call with bloggers Monday, McCain took Romney to task for being against the Senate's immigration measure. Romney's campaign dismissed McCain's remarks, saying they showed a candidate on the ropes over a politically volatile issue. McCain, long a backer of a comprehensive immigration overhaul, is a co-sponsor of the measure that would meld stronger border security with a guest-worker program and an eventual path to citizenship for many of the 12 million immigrants in the country illegally. Neither the measure nor McCain's backing of it sits well with hard-line conservatives. Romney, who has sought to position himself to the right of McCain on this and other issues, says he opposes the measure because it would allow virtually every illegal immigrant to remain indefinitely, and, thus, "is a form of amnesty." A year ago, he sounded more open to some illegal immigrants gaining legal status, telling a New Hampshire newspaper: "Those who've been arrested or convicted of crimes shouldn't be here. Those that are here paying taxes and not taking government benefits should begin a process toward application for citizenship, as they would from their home country." McCain made his comments after he was asked his opinion about GOP rivals opposing the Senate measure. Referring to Romney's stance, McCain said: "Maybe I should wait a couple of weeks and see if it changes because it's changed in less than a year from his position before." Then, with a chuckle, he made his cutting quip that referenced two embarrassing episodes for Romney in the past six months. Romney has faced criticism for calling himself a lifelong hunter even though he joined the National Rifle Association in August and officials in four states where he has lived said he never took out a hunting license. Defending himself, he said in April, "I've always been a rodent and rabbit hunter, small varmints, if you will." Also, The Boston Globe reported late last year that several illegal immigrants, including at least one from Guatemala, worked at the lawn care company that worked on Romney's two-and-a-half acre property in a Boston suburb for a decade. His aides have said that Romney was not aware of the workers' status, and that the owner was in the country legally. Romney spokesman Kevin Madden said his boss' opposition to the immigration measure has been clear. Madden counter-punched McCain, saying: "It seems that certain candidates who brokered this flawed plan are having a very difficult time grappling with or coming to terms with the political fallout that has ensued in a substantive manner." McCain also criticized Thompson for opposing the measure but didn't get nearly as personal as he did with Romney. "I was a little disappointed in Fred because, again, he had a different position not that long ago," McCain said in the conference call. "But since he's not a declared candidate, I think that Fred will be able to articulate his position." In a statement last week, Thompson said: "We should scrap this bill and the whole debate until we can convince the American people that we have secured the borders or at least have made great headway." But in a TV interview in 2006, Thompson appeared to advocate a comprehensive approach to dealing with the 12 million people living in the country illegally because deporting all of them "is not going to happen." A Thompson aide did not return a call seeking comment.