If we consider the situation of just 1-2 warheads are used in a conflict, I think it really hard to gauge the effect on public perception, and I suppose it also depends on the circumstances. If for instance, they were used in an unprovoked terrorist attack, killing 2-4million in a city, the response could be like after 9/11, but x100.
If they were used to stop a military aggressor, killing "only" 10k soldiers in the field, their may lose their mythical status, and this could be the opening of Pandora's box, increasing the probability that they are used in later conflicts.