In Vietnam, what assumptions had to be made in order to make a formless and frontless war possible and sustainable?

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.