not Robert Jones, but James Jones in 1988:

Behind L.B.J.'s Decision Not to Run in '68

By James R. Jones; James R. Jones, President Lyndon B. Johnson's chief of staff in 1968, was a Democratic Representative from Oklahoma from 1973 to 1987

Published: April 16, 1988

WASHINGTON — It's now just a shade over 20 years since Lyndon B. Johnson's speech to the nation that closed with this surprise: ''I shall not seek, and I will not accept, the nomination of my party for another term as your President.''

Most Americans couldn't believe that this larger-than-life figure could voluntarily relinquish the reins of power. Scholars and politicians still argue over what really motivated his decision to step down.

My perspective was that of the President's administrative chief of staff. My office was next to his. I can state categorically that fear of losing the 1968 election was not the reason he retired. Several days before the speech, Mr. Johnson commissioned a poll, which indicated that he would be re-elected over all possible candidates. I always have felt that he took that poll to satisfy himself that he wasn't being run out of office.

The real reason for Mr. Johnson's withdrawal was Vietnam. It was an involvement he had questioned as a Senator and about which he brooded as President. But his sense of Presidential continuity compelled him to pursue the commitments made by Presidents Dwight D. Eisenhower and John F. Kennedy.

As our casualties grew, the abstract agony caused by the daily situation reports became a personal pain for the President when his own son-in-law, Charles Robb, a Marine captain, entered combat.

In addition, Mr. Johnson had begun to doubt our ability to prosecute the war to any clear-cut victory. He worried about the discrepancy between Government reports and news stories in The New York Times written from Vietnam. The President mused aloud on more than one occasion that either The Times's reporter, R. W. Apple Jr., was working for the enemy or that our Government's intelligence apparatus was misleading him. ... (much more background in story)
During March 1968, LBJ was advised by his "Wise Men" that he was not going to achieve a clear-cut victory:

Johnson meets with 'The Wise Men,' March 25, 1968

On this day in 1968, as pessimism over U.S. prospects in Vietnam deepened, President Lyndon B. Johnson met with 14 informal advisers. In 1945, some of them had forged a bipartisan foreign policy based on containing the Soviet Union. They went on to craft key institutions like NATO, the World Bank and the Marshall Plan. They were known, collectively, as “The Wise Men.”

They met with LBJ after being briefed by officials at the State Department, the Pentagon and the CIA. They had been informed of a request from Gen. William Westmoreland, the top U.S. commander in Vietnam, for additional troops in the wake of perceived U.S. setbacks in the Tet Offensive.

Present at the White House meeting were Dean Acheson, George Ball, McGeorge Bundy, Clark Clifford, Arthur Dean, Douglas Dillon, Supreme Court Justice Abe Fortas, Averell Harriman, Henry Cabot Lodge Jr., Robert Murphy, Cyrus Vance and Gens. Omar Bradley, Matthew Ridgway and Maxwell Taylor.

In the words of Acheson, who summed up the recommendations from 11 of the men, “we can no longer do the job we set out to do in the time we have left, and we must begin to take steps to disengage.” Murphy, Taylor and Fortas dissented.
and from a PBS Transcript - first re: the Nov 1967 "Wise Men" meeting with LBJ:

McCullough: [voice-over] By the end of 1967, a grim sense of siege was settling over the White House. The President dug in. He had spent a lifetime climbing to the pinnacle of power; his whole political life now hung on only one issue -- Vietnam.

Clark Clifford: He decided to call in the men whom he respected most. They became known as "the Wise Men." There were about ten of them. If you put the total service, those men must have had two hundred and fifty to three hundred years of government service.

McCullough: [voice-over] These were the architects of American foreign policy -- Dean Acheson, John McCloy, Averell Harriman. "Contain Communism, don't let it spread" had been their advice to every President since Truman.

William P. Bundy: The picture that was given to them was that we are making slow, grinding progress and we thought we could see, at some point, a break, with the other side really starting to really weaken and go downhill.

McCullough: [voice-over] Dean Acheson said later, "I told him he was wholly right on Vietnam, that he had no choice except to press on."

Clark Clifford: They voted unanimously for him to go on with his course. He was greatly comforted by that.

William P. Bundy: The advice they gave was, "Look, the country doesn't see it the way you're describing it. You've got to develop a way to make your assessments of the situation more credible."

George Ball: Well, they gave him perfectly silly advice. They were sensible people, and why they were so silly, I don't know. Their main advice was, "Well, you ought to improve your public relations." Well, after the meeting, I spoke to Dean Acheson and John Coles and Arthur Dean, and I said, "You old bastards, you ought to be ashamed of yourselves. You're like a lot of vultures sitting on the fence and sending the young men out to die." And I walked out of the room.
but, the consensus disappeared in March 1968:

McCullough: [voice-over] By the middle of March, Clark Clifford despaired of ever changing the President's mind. Only one group of Americans might be able to influence him -- those foreign-policy experts called "the Wise Men". Five months before, the Wise Men had cheered Johnson with their support. Now, Clifford encouraged the President to meet with them one more time.

Clark Clifford: Although it might sound somewhat conspirational, I thought it wise to contact a good many of them first, so I did. I knew them all, I'd known them all for years, and I got a feeling from them. I made four, five or six contacts and found that in each instance, Tet had changed their minds. They all came back; we went through the same process -- reading cables, getting briefed; then we met with the President. They had all turned around. The impact was profound -- so profound that he thought something had gone wrong, and he used the expression "I think somebody has poisoned the well."

Richard Goodwin: He had picked these old Cold Warriors that were still fighting the battle of containment, and he listened to their advice, and as long as they stayed with him, he felt that he must be doing the right thing. Then, finally, at the end, they left him. They all said, "It's not working," and they walked out of the room, and there was Lyndon Johnson all alone with his war, the last believer.
So, that sums the evidence - although much more could be easily added (e.g., see Dean Rusk Transcript & George Ball Transcript).

Regards

Mike