Better bet is 1969 - an amendment to abolish actually passed the House overwhelmingly and polls of state legislatures indicated it had pretty good odds of full ratification. It also had the endorsement of both Nixon and Johnson, and the support of most interest groups - the Chamber of Commerce, the NAACP, and the League of Women Voters, for example.
It fell a few votes short in the Senate though due to a filibuster by Southern Democrats and weak support by Senate Republicans. Have Republicans back it completely (maybe as a result of a Humphrey victory despite losing the popular vote), and it could pass.