I think the reaction to 9/11 was quite different than that of the beginning of the Vietnam War, or of the Tet Offensive. 9/11 was a watershed event much like the assassination of JFK or MLK, or the bombing of Pearl Harbor. It changed the way a country felt and acted, almost universally, and almost all at once. Vietnam was perceived as a reaction to an abstract threat, with no attack ever coming close to the homeland.
While distinctly different events, some root reactions were the same. The shock and despair that took place after the September 11 attacks were quite similar to the experiences the American public felt was the Vietnam War progressed with no end in sight. The horrific realization of death was also present in both experiences. For the September 11 attacks, this experiences was seen on television and felt in the personal stories of lives being cut short. Vietnam brought home this experience when American families were being notified at an alarmingly high rate of loved ones or friends who had lost their lives or come back permanently changed from the Vietnam Conflict. Additionally, there was anger present in both. Americans were quite angry after being attacked on September 11, and a similar anger was seen during the Vietnam Escalation. This anger, however, was more directly aimed at the American government for its involvement in a war that was not fully understood and for being deceived in order to gain popular support.
I think that you can argue that the reactions were similar, though not identical.
In both cases, the US public was very supportive of the government and its military efforts. The 2001 reaction was more supportive but that is because the attacks were so public and so shocking. The start of the Vietnam War was much more gradual.
In both cases, the public approval dropped as the wars went on longer. The disapproval of the Vietnam War was much more vehement than the disapproval of the Iraq War, but the trend was similar in both cases.