Early in 1967, America was mired in an escalating war in Vietnam, presided over by President Lyndon B. Johnson. A collection of liberal leaders including anti-war Yale chaplain William Sloane Coffin, prominent socialist Norman Thomas and future Congressman Allard Lowenstein were determined to recruit a serious anti-war candidate to challenge Johnson in 1968.
They believed they had the perfect prospect: Martin Luther King Jr.
By 1967, King had gained stature as the nation’s preeminent civil rights leader. Against the advice of many, he was also speaking out against the Vietnam War, arguing that costly and immoral interventionism abroad was hindering progress toward racial and economic justice at home.
Source: Why Martin Luther King Didn’t Run for President – Rolling Stone