The Tet offensive was crushed by American forces as noted by previous posters; however it also indicated that the Viet Cong and North Vietnamese forces were much stronger and prepared to fight much longer than was previously believed. General William Westmoreland had constantly assured President Lyndon Johnson (who in turn assured the American public) that the U.S. was winning the war, and that ultimate victory was only a short time away. The Tet Offensive proved otherwise. It was the first indication that the U.S. was not winning, and in fact could not win the war. It was after that offensive that Secretary of Defense Robert McNamara informed President Johnson that the war was unwinnable. Had that fact been accepted at the time and the U.S. withdrawn, the end result would have been the same as when the U.S. did ultimately withdraw. The only difference was the large loss of U.S. soldiers, which could have been prevented had there been less hubris on the part of the American military.
While the Tet Offensive was certainly disheartening for those back home, in Vietnam it was an unqualified victory. The Vietcong were decimated as a serious fighting force and the North Vietnamese Army was responsible for the final victory. So you could say that the Tet Offensive was an argument to stay.
On the other hand, a majority of Americans wanted out of the war after Tet, and as the United States is supposed to b a representative democracy, you could also argue that the government should have followed the will of the people.
Nixon did begin the process of withdrawal in 1969, but this was a slower process than many in the US would have liked.
There was no reason to withdraw simply because of the Tet Offensive. This offensive ended up being a military defeat for the Vietcong and the North. It did not change the strategic outlook (militarily speaking) in the Vietnam War.
The only reason to pull out (assuming there was a reason to be there in the first place) was if the US public stopped supporting the war. This did not happen right away after Tet. Therefore, I don't think pulling out was necessary at that time (again, assuming that there was a good reason to be there in the first place).
But what I still am wondering is what would have the pros been, and what the cons would have been if America withdrew from the war right after the Tet offensive?