What was the glue that held the lmited war concept together with all its difficulties of thought and application?
This is going to be a complex answer. The wording of the question is insightful. There was a great smattering of "glue" that sought to keep intact the fragmented vision of limited war in Vietnam during the Johnson Presidency. This "glue" can be seen as comprising of different elements that conspired to preventing America from seeing the massive challenge that confronted it in the region.
One part of this "glue" had to be the belief of the intrinsic power of American military. Each stage of the increase in United States commitment during the Johnson Presidency operated with the belief that incremental growth will bring about success. Rolling Thunder was just that. The idea here was that the bombing capacity of the American military would cripple the Vietnamese. The glue was hope in the American air attacks, with sustained bombing would force negotiations. It failed to do so. The limited war theory was rooted in the idea that a small amount of American might in the form of military presence will yield results where the North Vietnamese would capitulate.
This same pattern can be seen in the increase in ground forces in the region. The growth of almost 200,000 troops in Vietnam was seen as the next step in the limited war theory. When Westmoreland demands and receives more troops, it becomes clear that the glue holding together this part of the vision was that the North Vietnamese could not possible fight off the presence of the Americans. This sentiment was shared at all levels of the military, the glue being the hope of American power would translate into American victory:
When we marched into the rice paddies on that damp March afternoon [in 1965], we carried, along with our packs and rifles, the implicit [unspoken but understood] convictions that the Vietcong would be quickly beaten.
At this point in the campaign, the "quickly beaten" idea is the glue that held together the vision of limited war in Vietnam. The erosion of this glue over time is where some of the greatest pain in the Vietnam War exists.
Finally, I would suggest that the last element of the glue in keeping this fragmented portrait of success in Vietnam in tact was the mere framing of the debate. Many of those who advocated full entry into Vietnam believed that limited war was needed in order to fight off the threat of Communism. This domino theory advocated that losing Vietnam would mean a loss of all other nations in the region. Additionally, there was a faulty logic in suggesting that Vietnam, as a nation, would take its Communist marching orders from China or Russia, something that was not accurate. It is in this paradigm that the limited war option was sought because American withdrawal would be perceived as "humiliating" to American worldwide presence.
This entire foundation is not where the Vietnamese saw this struggle. Whereas America saw the war as a battle for Communism, the Vietnamese saw it as a fight for autonomy and freedom from all external control. America's own history can speak to the power and galvanizing notion of a fight for independence. American logic at the time never saw this as that. Instead, they perceived that the Vietnamese were going to become a puppet of the larger brand of Communism, which was not going to be the case. This theoretical underpinning became another aspect of the glue that held the acceptance of the limited war theory together in Vietnam.