It seemed as if it would have made sense.
There was no chance that the United States would use nuclear weapons during the Vietnam War. Here are a few reasons why:
By the 1960s, the Cold War had evolved into a stalemate enforced by thermonuclear ICBMs. The United States could not use use a nuclear weapon anywhere in the world without threatening nuclear war with the Soviet Union.
The United States fought a limited war in Vietnam, always weary of drawing China into the conflict. Bombing Hanoi (the capital of North Vietnam) was risky enough; an invasion of North Vietnam and occupation of Hanoi was off the table altogether. Nuclear weapons also contradicted the logic of this limited war.
Even without the threat of Soviet or Chinese intervention, nuclear weapons could not have realized American goal in Vietnam of ending the insurgency in South Vietnam and stabilizing the government there. Sure, the United States used conventional bombs as a deterrent in North Vietnam in an attempt to curb Hanoi's support for the Viet Cong, but a nuclear attack would have only further destabilized the region and most certainly would have undermined the American attempt to win the "hearts and minds" of the Vietnamese people, central to the American strategy of realizing regional stabilization.
Check out this other related question. It was considered in an abstract way, but the political consequences (alienating all allies) and even strategic consequences (putting tactical nuclear weapons "on the table" would hurt the US more than not) all were very strongly against it.