It's also debatable that he didn't run in 1968 because he felt he was unpopular.
Lyndon B. Johnson is one of the most underrated Presidents in history. He did a lot of good for the country.
http://www.u-s-history.com/pages/h1862.html
Not exactly. By1967 the social programs became nationally divisive, and the war was magnifying all the tensions in the extreme. By late 1967 Johnson couldn't go anywhere without meeting significant harsh protests, and the Democratic party had split much more seriously than Republicans today. The Tet Offensive tipped feelings against Johnson dangerously. Though the North Vietnamese were decisively beaten, media coverage showing how much reach they had over South Vietnam led to broad conclusions among Johnson's advisors and most of the public the war could not be won, meaning stalemate at least. Famously even Cronkite seemed to drop the view the war could be won. Certainly with the Korean War stalemate still fresh in American minds at the time the view Vietnam would end the same way made the war and more American deaths look futile.
Bobby Kennedy at the time was not the factor at first he seems today. His candidacy was considered a long shot and it was Eugene McCarthy at first who demonstrated his strength by nearly beating Johnson in the New Hampshire primary, though it's impressive Johnson's support was by write-in because he had not declared his intentions.
http://articles.latimes.com/2008/mar/30/opinion/op-jones30
Don't forget it's widely believed Johnson and his administration set up the Gulf of Tonkin incident to escalate tensions into commitment for war. If you read the article it alludes to how Johnson felt about his personal responsibility for all the American deaths.
Yes, Johnson is much more highly regarded today, but his popularity by 1967 already had made re-election look very difficult. Before Tet some Democratic governors were warning Johnson would lose their states. After Tet more of the public was against Johnson and the splits in the Party made re-election very doubtful. Today because he had made very tough social program choices against harsh resistance he often ranks in the top 1/3 or 1/4. Sometimes better.
Walter Cronkite
https://www.youtube.com/watch?v=Nn4w-ud-TyE