The American public's opinion of the war deteriorating over time.

The Tet Offensive in of itself was a huge factor. We were viewed as invincible, and the war nearly over, then all of a sudden there were PAVN soldiers in the US Embassy at Saigon. That didn't help bolster the public's confidence in the war much, and many thought that we were now losing the war, or had been for a long time and the American generals just hadn't told anyone.

The most influential single event was the My Lai Massacre during the Tet Offensive. American soldiers, frazzled from fighting for two straight months barged into the village of My Lai in March '68 and murdered anywhere from 350-500 Vietnamese men, women, children, and infants. The event was covered up until November '69, and was a huge source of public outrage when it was released. The aftermath included all of the soldiers involved being acquitted with the exception of Lt. William Calley, who had his lifetime prison sentence shortened to three months in the pen and three and a half years of house arrest. The three soldiers who blew the whistles on the whole shebang were shunned from the military and even denounced as traitors by Mendel Rivers, Chairman of the House Armed Services Committee. They received medals 30 years later, posthumously for one soldier.

There were a lot of things that played a part, such as the opposition to the draft, the new style of reporting that showed the US the gore and violence of warfare, effectively eliminating the myth of the glory of war, and some people really hated the idea of the "Domino Theory" in general. However, if you're looking for a specific event that swayed a huge amount of public opinion in one fell swoop, it's the My Lai Massacre in specific and the Tet Offensive in general.