There were some within the US policy establishment that advocated for the use of tactical nuclear weapons in Vietnam. The reasons to oppose such a policy were many. From a political standpoint, it would have alienated the already-alienated American allies and domestic public, and could easily have led to an escalated role with (nuclear-armed) China (which is why the US did not contemplate invading North Vietnam). Any strategic use of the weapons (e.g. bombing North Vietnamese cities) would have incurred international outcry, condemnation, and possibly sanction, at the very least.

From a tactical standpoint, it is unclear that nuclear weapons would actually produce victory, or would be of much utility against such an enemy (tactical nuclear weapons are useful against massed columns and fixed positions, not diffused troops hiding in jungles). Lowering the threshold for nuclear use would only in the long run (and maybe the short run) hurt American interests — the US and its military were far more vulnerable to such weapons than the Vietnamese, and the US benefited from the assumption that such weapons would not be used regularly in warfare.

For many more details and discussions, see Nina Tannenwald, The Nuclear Taboo, which has a chapter on Vietnam.