Tet Offensive and Fourth Generation Warfare

Even though the Vietcong were materially defeated in detail, they won the moral victory, says Robert Greene:

Within a few weeks, in all parts of South Vietnam, the Americans regained the upper hand, retaking control of Saigon and securing their air bases. The sieges at Hue and Khe Sanh took longer, but massive artillery and air bombardments eventually doomed the insurgents, as well as leveling entire sections of Hue.

After what later became know as the Tet Offensive was over, Westmoreland likened it to the Battle of the Bulge, near the end of World war II.  There the Germans had managed to surprise the Allies by staging a bold incursion into eastern France. In the first few days, they had advanced rapidly, creating panic, but once the Allies recovered, they had managed to push the Germans back -- and eventually it became apparent that the battle was the German military's death knell, their last shot. [...] The entire Vietcong infrastructure had been wiped out.

[...]

But another viewpoint began to trickle in from home: the drama at the U.S. embassy, the siege of Hue, and the attacks on air bases had kept millions of Americans glued to their television sets. Until then the Vietcong had operated mostly in the countryside, barely visible to the American public. Now, for the first time, they were apparent in major cities, wreaking havoc and destruction. Americans had been told the war was winding down and winnable; these images said otherwise. Suddenly the war's purpose seemed less clear. How could South Vietnam remain stable in the face of this ubiquitous enemy? How could the Americans ever claim a clear victory? There was really no end in sight. 

American opinions polls tracked a sharp turn against the war. Anti-war demonstrations broke out all over the country. President Lyndon Johnson's military advisers, who had been telling him that South Vietnam was coming under control, now confessed that they were no longer so optimistic. In the New Hampshire Democratic primary that March, Johnson was stunned by his defeated by Senator Eugene McCarthy, who had galvanized the growing antiwar sentiment. Shortly thereafter Johnson announced that he would not run for reelection in the upcoming presidential race and that he would slowly disengaged American forces from Vietnam

The Tet Offensive was indeed the turning point in the Vietnam War, but not in the direction that Westmoreland and his staff had foreseen.