When her husband died suddenly in office on January 7, 1964, Baker ran as a Republican in the special election to fill the remainder of his term, defeating Democrat Willard Yarbrough, a Knoxville journalist. As a candidate for the seat, she promised to serve only as a caretaker who would not seek further election; and she fulfilled that promise, and served from March 10, 1964, to January 3, 1965. While in Congress, she served on the House Committee on Government Operations and advocated for a balanced federal budget. She also championed coal mining interests, the TVA, U.S. Atomic Energy Commission programs in Oak Ridge, Tennessee, and cost of living increases in Social Security pensions. As one of ten Republicans from the South, she voted against the Civil Rights Act.