Well she did detonate a nuclear warhead with a rock :o)
But seriously, anyone on the island should be killed by the bomb going off. Obviously they aren't going to do that though. The question is not really how they survive, but rather where/when they end up as a result of the explosion.
However Juliet might just be a special case. She was seperated from the others and very badly injured (from the fall). She might end up with/when the other losties but I'd suspect she'll either be dead, or die soon after.