@: Invading North Korea
1. No doubt the US could do it with or without help from any other country.
2. It would not be a quickly won war, it would be similar to the first Korean war, jungle warfare in land they know better and have extremely fortified.
3. The population of Korea wouldn't like us there, this is a country run by fear, a North Korean that chooses to help the US troops could very well end up tortured and his whole family murdered. Its not because they hate us, but they hate having to choose a side.
4. Despite our technological advantage, we can't just full on scorch the earth. We have to consider civilians, yeah we could napalm carpet bomb and nerve gas strike them, but collateral damage would be too high. And the North Korean military would know this, civilians = shields. We've come a long way from wearing color coded uniforms and standing in open fields firing at each other.
@: Actually doing it.
Doubt it. After their stunt, North Korea is basically saying "haha you can't do anything about it!" while they have Seoul dangling over a fire pit. They're also probably feeling pretty badass thinking, see they really can't touch us!
The only possible thing that would cause an inevitable steamrolling would be if North Korea does something that absolutely crosses the line, they need to do something bigger (and directed at Americans) before the mass media starts making noise. Otherwise China, as the unfortunate neighbor, would take action instead of us.
~Darkrider2