If someone really wanted to invade North Korea, they'll be doing it while making sure South Korea won't simultaneously be wiped out.
Probably the most fit country at this moment among the potential combatants to invade, occupy, pacify, and then rebuild North Korea is South Korea itself, and it is also the most fit to defend itself under that unification war scenario, if given the proper political leeway to acquire the necessary military weapons, considering all the political, economic, military, geographic, demographic, social and cultural factors.
But we still prefer more to unify through non-violent means in a more gradual process, and that is in the best interest of every country in the region, including the United States. Another war like Iraq or Afghanistan (possibly worse) is something that the US can ill-afford at this moment, when its war in the Middle East isn't done yet and is struggling to get its economy back in shape. The US is seeking to significantly cut down on defense expenditure for the next few years and another large-scale war across an intercontinental distance is in direct confrontation with that objective.
I have doubts that the United States could win without the use of nuclear weapons. They couldn't win in 1950, they won't win in 2011.
People seem to think that technological advantages can win a war; Korea and Vietnam have long since proved that wrong.
The US didn't have a real technological advantage in 1950 over the USSR backed North Korea. Today, the gap is absolutely incredible and I doubt - I sincerely doubt - that it would take more than a week to get to Pyongyang with the amount of troops currently there and in Japan. Absolute air superiority is key and North Korea wouldn't stand a chance if the US/SK struck first.
However, if NK struck first or had time to prepare, Seoul would be decimated.
Now, battle of hearts and minds? That's a totally different story.
They had the same large technological gap now as they did in Vietnam and the Korean war. In both wars, the U.S had absolute air superiority.
In Vietnam, the U.S had infinitely better equipment (with helicopters) but they couldn't clear out their determined foe due to the terrain, which is similar to Korea's terrain.
The airpower argument is largely moot, as the north koreans have a very strong and relatively sophisticated radar based anti aircraft network of SAMs. U.S bombers would be shot down by SAM sites that are easy to hide. Remember Israel's Yom Kippur war, they lost more than a hundred modern aircraft to SAM sites in Egypt. The number of stealth bombers is low enough to be considered a nonfactor, with costly and recurring maintenance required.
The Korean airforce is numerous and will be able to operate with the protection of their SAM network, they do have some MiG-29 and 23s which are more than capable of destroying american aircraft. The Americans would probably be operating FA-18 hornets out of their carriers and from their Japanese bases, which are no match for SAMs and MiG 29s.
The North Korean ground forces (totaling 7,700,000 with their pulled reserves) would outnumber the active south korean army by a factor of 11, and they would take Seoul on the first day. There would be no Pusan perimeter this time, they would have Pusan by week 2
If the north koreans can kill one U.S soldier for every ten of theirs, then the U.S will no longer be willing to fight the costly overseas war during their period of economic issues.
"You can kill ten of my men for every one I kill of yours, but even at those odds, you will lose and I will win."