The best counter arguments to the nuclear option can be found in the 1967 JASON committee’s 60-page report entitled “Tactical Nuclear Weapons in Southeast Asia”.
Within it, the committee finds that tactical nuclear weapons would have had limited results in Vietnam. Nuclear weapons are most useful against large massed troops. But the Vietnamese communists didn’t fight the US with massed troops. They used small guerrilla units.
Therefore, nuclear weapons would have done little more than conventional bombing campaigns, which were already proving ineffective against an enemy that appeared to disappear into thin air.
The JASON committee estimated that to totally wipe out the Northern Vietnamese forces and their supply lines in small tactical attacks (as Goldwater suggested) it would require 3,000 tactical nukes a year.
On top of that, the fallout of nuclear weapons would be unpredictable and difficult to control. It could affect the Southern Vietnamese population just as adversely as it would the enemy communists.
The use of nuclear weapons also came with significant risk. It could be seen as an escalation of the war effort, and prompt China or the USSR to enter the war.