His first name commemorates the framing of the United States Constitution in 1787, the year of his birth.

He was elected to represent Ohio's 14th congressional district in the 22nd United States Congress in 1831 as an anti-Jacksonian candidate.

He was not reelected to this office, notwithstanding his receipt of a majority of votes.

While he was in Congress, fellow Ohio Representative William Stanbery was assaulted on the street by General Sam Houston, in consequence of remarks made on the floor of the House.

In bringing the matter before Congress, Cooke said that if he and his friends were denied protection by that body, he would "flee to the bosom of his constituents," and this expression was taken up by his political opponents and remained a catch word for some time.