Norris was elected as a Democrat to the Twenty-eighth and Twenty-ninth Congresses (March 4, 1843 – March 3, 1847). He was again a member of the State house of representatives in 1847–1848, and served as speaker. He was then elected to the U.S. Senate and served from March 4, 1849, until his death. While in the Senate, he was chairman of the Committee on Claims (Thirty-first Congress) and a member of the Committee on Patents and the Patent Office (Thirty-second Congress) and the Committee on the District of Columbia (Thirty-third Congress). He died in Washington, D.C., in 1855; interment was in Floral Park Cemetery, Pittsfield.