What happened was that LBJ realized after the Tet offensive that he could no longer get the troops to fight the stupid war. They had to draft six or seven boys to get one soldier, and enlistments were plummenting.
Nixon had no choice but to "Vietnamize" the war. Johnson simply did not wish to preside over a defeat. Nixon was stuck with the same problem, but by the time he took over, there was a shortage of gung-ho yokels that would willingly enlist or allow themselves to be drafted.
Nixon knew he could not escalate the war, because it would become obvious that would be draftees would have to be arrested and impressed by force into the military. That would have revealed a major weakness to the entire world. I had dozens of friends who said they would prefer jail or permanent exile in Canada to fighting a useless and unwinnable war in Vietnam.
Nixon could have ended the war by 1970 or earlier, with no worse results than the rather humiliating rout that happened. Everyone who died in Vietnam died for no good reason, and both LBJ and Nixon were responsible. But Nixon was elected because he claimed he had a "special plan", which was a lie, and he was impeached and out of office by the time the war was over.