As he continued to serve, the atmosphere of the 1960s weighed on Anderson and he began to re-think some of his beliefs. By the late 1960s, Anderson's positions on social issues shifted to the left, though his fiscal philosophy remained largely conservative. At the same time, he was held in high esteem by his colleagues in the House. In 1964, he won appointment to a seat on the powerful Rules Committee. In 1969, he became Chairman of the House Republican Conference, the number three position in the House Republican hierarchy in what was (at that time) the minority party.