The Democratic Party had historically dominated Texas, but Republicans scored their first major victory in the state with John G. Tower's victory in a 1961 special election to the United States Senate. Motivated by Tower's victory, and hoping to prevent the far-right John Birch Society from coming to power, Bush ran for the chairmanship of the Harris County Republican Party, winning election in February 1963.[54] Like most other Texas Republicans, Bush supported conservative Senator Barry Goldwater over the more centrist Nelson Rockefeller in the 1964 Republican Party presidential primaries.[55]
In 1964, Bush sought to unseat liberal Democrat Ralph W. Yarborough in Texas's U.S. Senate election.[56] Bolstered by superior fundraising, Bush won the Republican primary by defeating former gubernatorial nominee Jack Cox in a run-off election. In the general election, Bush attacked Yarborough's vote for the Civil Rights Act of 1964, which banned racial and gender discrimination in public institutions and in many privately owned businesses. Bush argued that the act unconstitutionally expanded the powers of the federal government, but he was privately uncomfortable with the racial politics of opposing the act.