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.