In 1918, Democrat McGlennon, then majority leader of the state senate, defeated Republican William Ross by just 299 votes out of more than 25,000 cast. McGlennon was then the elected representative to the 66th United States Congress (March 4, 1919 – March 3, 1921), representing New Jersey's 8th congressional district in the United States House of Representatives, but was an unsuccessful candidate for reelection in 1920 to the 67th United States Congress. He served as a delegate to the 1920 Democratic National Convention. In 1924, he was appointed judge of the New Jersey Court of Errors and Appeals and served until his death. Cornelius also was acting supervising principal at Harrison, New Jersey from 1926 to 1931.