Wheeler was elected to represent the First District in the U.S. House of Representatives. He served in the Fifty-fifth, Fifty-sixth, and Fifty-seventh Congresses (March 4, 1897 – March 3, 1903). Wheeler secured significant appropriations for projects in his district, including the expansion of a federal courthouse in Paducah and the protection of a local ice harbor.
Wheeler was elected to represent the First District in Congress. During his time in office (March 4, 1897 – March 3, 1903), he secured substantial funding for projects in his district, including the construction of a federal courthouse in Paducah and measures to safeguard a local ice harbor.