In 1996, Thibodaux launched a third campaign for the 7th District seat. Hayes switched to Republican affiliation and vacated his House seat to seek the open U.S. Senate position in 1996. With the 7th Congressional seat open, Thibodaux saw the election as the best opportunity for a Republican to carry the 7th district for the first time. Under the unique Louisiana primary system, Thibodaux lost a spot in the general election against Democrat Chris John by only twelve votes. On election night, Thibodaux was projected as finishing in second place, ensuring a spot in the general election, over 200 votes ahead of the third-place finisher Democrat Hunter Lundy. However, after a week of ballot recounts, John led with 45,404 ballots (26 percent). Lundy trailed with 38,605 votes (22 percent), just 12 votes ahead of Thibodaux's 38,593 votes (also 22 percent). While Thibodaux was the endorsed Republican candidate, three other Republican candidates campaigned as well. The presence of the three other Republicans, Jim Slatten, Peter Anthony Vidrine (born November 1957) of Ville Platte in Evangeline Parish, and Charles "Charlie" Buckels, with a total of 25,840 votes (15 percent), cost Thibodaux an opportunity to enter a face-to-face showdown with John in the general election. Vidrine ran unsuccessfully for the Louisiana House of Representatives for District 38 in 2011 and subsequently joined the Constitution Party.