Harris was born in Cotton County, Oklahoma. He graduated from the University of Oklahoma in 1952 and its law school in 1954. He was first elected to the Oklahoma State Senate in 1956 and served in it until 1964. For most of this time he was one of its youngest members. He made an unsuccessful race for governor of Oklahoma in 1962; however, he became better known throughout the state as a consequence of this race.

In 1964 Harris entered the race to serve out the unexpired term of United States Senator Robert S. Kerr, who had died in office. He was successful and was sworn in as soon as the vote totals could be verified, becoming, again, one of the youngest members of the body in which he was serving. Despite being fairly liberal from a generally conservative state, he was elected to a full term in 1966. During this Senate term, he also served briefly as chairman of the Democratic National Committee, being both preceded and succeeded in that position by Larry O'Brien. Harris was also on the short list for Vice-President in 1968 when Hubert Humphrey narrowed his choices to Harris and Senator Edmund Muskie of Maine. Humphrey eventually chose Senator Muskie.

Harris did not seek another term in 1972, choosing instead to make a run for President. It was a short-lived campaign that ended with Harris planning a different kind of race in 1976. In 1975 he announced that he would seek the Democratic Presidential nomination in 1976. Harris' race had at least two unusual features. For one, in order to keep expenses down, he travelled the country in a RV and stayed in private homes, giving his hosts a card which was to be redeemable for one night's stay in the White House upon his election. For another, he placed unusual stress on issues affecting Native Americans. This was due to his backgroud - his wife LaDonna Harris was of Native American ancestry, and he was from the state which had begun its political existence as Indian Territory. Harris' positions on issues were largely those of an unabashed liberal; he appealed to the party's activist base which had helped to nominate George McGovern in 1972; this stand had considerably less appeal to major contributors who had observed McGovern's 49- state landslide defeat four years earlier and were looking for a candidate who seemed more electable. Harris' underfunded campaign soon faltered; along with his inability to raise significant sums of money his support among the party's liberal activist base was split with Arizona Representative Morris Udall. (The nomination and eventual November victory went to former governor of Georgia Jimmy Carter, who ran as a moderate.)

Harris left elective politics for the academic world. He has had many books on political subjects published, including, Potomac Fever (Norton, 1977 ISBN 0393056104) and Deadlock or Decision: The U.S. Senate and the Rise of National Politics (Oxford University, 1993 ISBN 0195080254). He is also the author of three novels. Harris currently is a professor of political science at the University of New Mexico and a resident of Corrales, New Mexico.