In Vietnam, what assumptions had to be made in order to make a formless and frontless war possible and sustainable?
I think that there were plenty of assumptions that had to be made in order to drive the war effort into the realm of sustainability. The most powerful of which involved defining victory through a different matrix than the American public had ever used in assessing military successes. Prior to Vietnam, the definition and the calculations for victory were fairly clear. Yet, in Vietnam, it became critical for the United States public to understand that "victory" in the traditional sense was not possible. The goal of the campaign seemed to be one based on attrition of the enemy forces to a point where their impact would be a negligent one. Such a definition of victory is different and one that the public never fully embraced. Part of the reason for this is that it was such a difficult concept to grasp in the "fog of war" where emotions and insecurity are at such a high and strong level. In defining victory in this manner, it allowed the United States to continue in the engagement of a formless and frontless war where the enemy and their location is amorphous and far from definite.
I completely agree with the first answer -- one of the major assumptions was this new definition of victory. Along with this assumption, however, there had to be another one. This was the assumption that communism was such a threat that an amorphous war like the one you mention could and should be continued indefinitely. Because the goals of the war were so vague, the American people had to believe that there was a significant threat that would make the fighting important enough to continue, even with no clear way of achieving victory.
A second assumption was that victory was possible through military action. The American government and people had to be convinced that the US could achieve its goals through military force even though those goals were more political in nature (to allow S. Vietnam to be a stable and non-communist country).
These assumptions were both necessary in order to make this new kind of war seem feasible.