No, we were actually winning the war. The Tet Offensive was a desperate attempt to change the direction of the war. The result was that a large portion of the VC was wiped out in the mistaken belief that the offensive would cause a popular uprising supporting them. Unfortunately, it was portrayed as a defeat for us, but the reality on the ground was much different. Once Walter Cronkite declared the war unwinnable, public and political support started to decline rapidly.
Here is a good site to track the timeline of the war in Vietnam
It wasn’t about Walter Cronkite. It was seeing that the enemy was still capable of mounting attacks simultaneously across the entire country, and nearly overrunning our embassy that made people stop and wonder.
You weren’t in the US, but what caused the public and popular support to decline rapidly was not only the Tet offensive, but, even more importantly, the end of student deferments. Once middle class and upper class kids lost their exemption from military service, their parents started asking much more serious questions about just what was going on in Vietnam. That was the beginning of the end of the war.