While in the legislature, Jenkins organized and served as chairman of the Conservative Caucus in the state house, which had begun with only four members in 1972. By 1980, a caucus member, John Hainkel of New Orleans, was elected House Speaker. Jenkins served as chairman of the House Committee on Labor and Industrial Relations. Jenkins personally favored right-to-work legislation, but voted against a 1976 right-to-work bill signed into law by Governor Edwin Edwards due to the large number of union workers who lived in his House district.