They will get just that. First off, Obama is a creature of the polls. An actual by-God nuclear strike by NOKO will create a clamor to slap them down in the United States. Although it has now been forgotten, after 9-11 there were lots of Dems good with turning Afghanistan into a vast glass-bottomed plain. (So long as we didn't send — you know — ground troops.) So Obama will have to make a military response. Or lose the next election. (Can't have that.)
If he is smart, he will let the US military do its thing, and we will see something very similar to what happened in Afghanistan in 2001-2002. Then the invincible Taliban, aided by that equally invincible general, Brutal Afghan Winter, got their heads handed them by Special Forces and American airpower. Same thing will happen here. Mr. Smart Bomb meet Mr. NOKO Armor, and Mr. NOKO Command Bunker, and Mr. NOKO Nuclear Facility and Mr. NOKO . . . Any NOKO offensive will grind to a halt almost immediately. And then their army will starve, because they have no food reserves. And the NOKO nukes will prove to be ineffective and NOKO long dongs impotent (the missiles — get your mind out of the gutter) and anyone else possessing nukes or trying to get nukes will think twice, because the US will have proved that nukes don't make you invincible — even if your opponent doesn't respond with nukes.
Or if Obama plays it the way I think he will (stupid) he plasters NOKO with our nukes — turning the northern half of the peninsula into something that glows in the dark. Same result for NOKO, albeit a lot of fallout (literally and politically for the US).
Or Obama may do a “hommina-hommina” act, and the the NOKO army rolls into the South, gets stop-punched by the South Korean army, starves (as above), and the South Koreans then roll into the north, get greeted as liberators, and sign some kind of deal with the PRC to keep the whole country. (After all, why should South Korea ally with an impotent Obama-led US, when they can get China's protection?)
Any way it is played an actual war brings NOKO disaster. No, their game is to see how much lunch money they can bully short of starting fists swinging. Just like bullies back in elementary school.