President Lyndon B. Johnson Justifies His Decision Not to Run Again, Believing It Will “Unite Americans and so advance the day of peace.” 

He sees "no higher or more urgent interest..."

The military escalation in Vietnam deflected attention and funding away from President Johnson's domestic programs, resulted in sharp inflation, and prompted rising criticism and protests about the wisdom of the war. But President Lyndon B. Johnson believed in the war, and to a degree staked his presidency on it.

As 1968 dawned, nobody doubted that Johnson would run for a second term as President, and indeed his name was entered in early primaries with his consent. However, early 1968 was tumultuous and events were fast-moving and unpredictable.  On January 30, the North Vietnamese launched the massive Tet Offensive, a surprise attack on South Vietnamese and American forces that reached from every province in Vietnam right into the American embassy itself. Although U.S. and South Vietnamese forces claimed victory based on repulsing the attacks and body counts, the Tet Offensive made the American people realize that their opponent was stronger and better organized than had been previously realized, and that the light (a military victory) was not visible at the end of the tunnel, as had been promised.  Meanwhile, this turn in the struggle made Johnson even more secretive, determined, and hypersensitive to criticism. Then, on March 12, 1968, came the New Hampshire primary, in which Johnson was opposed by Sen. Eugene McCarthy, an outspoken foe of the war but a virtual unknown lacking any funds or any sense of charisma. Johnson had done well in New Hampshire in the 1964 election, and it was anticipated that he would clobber McCarthy, and that if McCarthy could gain any appreciable vote it would be a miracle. Johnson won, all right, but it was a narrow victory (McCarthy received over 40% of the vote) that showed how vulnerable Johnson was.

Some of Johnson's closest advisors now counseled de-escalation in Vietnam. Confronted by mounting opposition, on March 31, 1968, Johnson stunned the nation with two surprise announcements: he would stop the bombing in most of North Vietnam to seek a negotiated end to the war, and he would not run for reelection. LBJ, who had so hungered for the presidency, in the end had had enough. He received many expressions of support for this move, one of which was from Nevada Sen. Howard Cannon.

Cannon wrote him and received this explanation for LBJ’s decision not to run. Typed Letter Signed, on green White House letterhead, Washington, April 8, 1968. "I am proud to have your continued confidence, but I have the faith to believe that it will prove wise and healing in helping to unite Americans and so advance the day of peace. There is no higher or more urgent interest. I ask your hand in this vital purpose, with all gratitude and hope."

Vice President Hubert Humphrey entered the suddenly-open Democratic race with the support of the party establishment, and Robert Kennedy, like his brother before him, planned to win the nomination through popular support in the primaries. So Kennedy was felled by an assassin, and Humphrey was defeated by Richard Nixon. As for the war, it continued for another five years.