South Korea will reject any possible offensive military action against North Korea, SK can't take the risk of being toasted like a fat goose by cannon storm from the caves of their northern brothers. This will completely destroy their economy. US will have to seriously consider the consequence of such move, small European members of NATO will understand they're probably next toasted goose if there's any escalated collision between Russia and NATO, this will definitely trigger the collapse of NATO.
The best bet of US and South Korea is that North Korea will have an internal coup, the fat Kim understands his rival's intention and psychology very well, that's why North Korea employ a strict isolation policy and national spies are at every corner of North Korea.
This is a game of psychological endurance, if US can't hold, South Korea will lose and hence US will lose, if North Korea can't hold, Kim will lose.
All the news and propaganda are for those North Koreans who have a secret channel to access outside information like this, this will gradually accumulate North Korean's internal force for a potential coup.