Cooper described himself as "a truly terrible public speaker" and rarely made addresses from the Senate floor. He was known as an independent Republican during his career in the Senate. In the first roll-call vote of his career, he opposed transferring investigatory powers to Republican Owen Brewster's special War Investigating Committee. His second vote, directing that proceeds from the sale of war surplus materiel be used to pay off war debts, also went against the majority of the Republican caucus, prompting Ohio Republican Robert A. Taft to ask him "Are you a Republican or a Democrat? When are you going to start voting with us?" Cooper responded, "If you'll pardon me, I was sent here to represent my constituents, and I intend to vote as I think best."