Dornan made headlines in March 1985 for a confrontation with Representative Thomas Downey (D-NY) on the House floor. Downey asked Dornan about comments he had made calling Downey "a draft-dodging wimp." According to Downey, Dornan, grabbing him by collar and tie, said, "It's good you're being protected by the sergeant-at-arms. If I saw you outside, it would be a different story" and threatened him "with some form of bodily harm." Dornan claimed he was merely straightening Downey's tie and refused to apologize for the incident or the derogatory comment. A Dornan aide said, "It will be a cold day in hell before he gets an apology from Bob Dornan."
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In 1995, he received a minor reprimand from the House for stating in a floor speech that President Bill Clinton had "given aid and comfort to the enemy" during the Vietnam War. In 1996, Dornan ran for President of the United States, using his campaign primarily as a vehicle to continue to criticize Clinton. In a GOP debate in Iowa on January 13, Dornan called Clinton a "criminal" and a "pathological liar." When asked why voters should choose Dornan over his Republican rivals to challenge Clinton in the general election, he argued that he had more children and grandchildren than the others, with only Richard Lugar coming anywhere near him on that score