The North Vietnamese had several hopes for Tet that were not accomplished including an uprising by the South Vietnamese population, None the less I do not consider that they "lost" or more importantly that the US "won". Tet destroyed claims by Westmoreland and Ambassador Ellsworth Bunker that there "was light at the end of the tunnel". Rather it was clear that even the US Embassy was not safe from attack. The strategic hamlet program was a failure. American military bases were not safe from attack. As we latter learned in Westmoreland's lawsuit against CBS he was deliberately underestimating enemy troop levels. The problem Westmoreland and Wheeler faced in early 1968 was not one of bad press coverage; it was their rosy assessments were no longer credible. The basic problem was that the majority of the people did not support the South Vietnam regime, did not share our view of what a free society should be and did not want us around. The Army's long term response to the problem was to better control what correspondents saw during the Gulf War coupled with a commitment by Colin Powell to tell the absolute truth.Tet failed in it's objective - which was to try and provoke a general uprising amongst the South Vietnamese population against the South's Government. The NLF was meant to occupy, around Saigon the likely landing grounds for US Helicopters and so prevent the rapid reinforcement of the US and ARVN forces in the city. They failed.
What could the US have done in 1968? I assume nucs were off the table. An invasion of North Vietnam would have lead to a long term occupation plus the risk of Chinese intervention. Moving to occupy the Ho Chi Minh trail would have lead to the same results.