It's more likely that the UN Security Council will meet and agree that North Korea's plans for an expanded nuclear arsenal represent such a serious threat that a military intervention would be justified.
That might sound like an extreme scenario, and it is. But North Korea have nuclear weapons, they have the ability to launch satellites into orbit, and they have threatened to attack the US mainland. If ever they were to marry all three and create an ICBM, then they'd stop being a threat to South Korea and start being a threat to everyone. They're square in the middle of the single greatest concentration of population on the face in the earth. Even if they would be unlikely to target some of these cities, they would theoretically be able to reach Tokyo, Guangzhou, Seoul, Jakarta, Shanghai, Delhi, Karachi, Mumbai, Manila, Osaka, Beijing, Kolkata, Dhaka, Bangkok, Shenzen and Tianjin - over three billion people. And that's just counting the population of the cities themselves. More than half the world's population would live within targeting range of a rogue nation with a leader who gets more and more unstable as he gets more and more confident. And on top of that, North Korea has along memory when it comes to enemies. They've hated the United States for six decades; do you think they're going to forget all of the nations that imposed sanctions on them so quickly?
So you can understand why the United Nations would be keen to pull North Korea back in line before then. Nobody wants to resort to a military option, but when push comes to shove, it might be the only option.