We will never know what the effect of going nuclear on Vietnam would have had on the Cold War and the world, but I doubt that it would have been pretty, it probably would have led to a massive acceleration and hardening of the global war footing and a more desperate search for a way to survive once an unstable, renegade America was revealed as a threat to everyone, and every city on the planet.
By the way, we had already lost 400 men before 1965.
They Soviets would have stayed quiet. In 1965 we had 854 ICBMs, 384 SLBMs and 650 strategic bombers. The Soviets had 281 ICBMs, 75 SLBMs and 163 strategic bombers. By retaliating for the nuclear strike in Vietnam, the Soviets would be commiting suicide.