Goodell was re-elected in November 1960 to the 87th Congress, and re-elected three times thereafter. During his tenure in the House, Goodell voted in favor of the Civil Rights Acts of 1960, 1964, and 1968, and the Voting Rights Act of 1965, but voted against the 24th Amendment to the U.S. Constitution. He resigned on September 9, 1968, to accept Governor Nelson A. Rockefeller's appointment to the United States Senate, filling the vacancy caused by the assassination of United States Senator Robert F. Kennedy on June 5, 1968. Because a special election to fill the vacancy would not be held for over two years, public objection to the length of Goodell's appointment led to a failed legal challenge to the Governor's power to appoint Senators in the event of a vacancy, "Valenti v. Rockefeller".