What would the United States do if we were attacked by... let's say the Mexican Army (instead of just an army of Mexicans sneaking across our southern border)? Imagine that Felipe Calderon lost his mind (just like North Korea's Kim), and began lobbing artillery shells into Arizona, California or Texas. What would our response be? Would our "president" issue a statement condemning such an action, and threaten that a strongly worded letter will follow? Obama probably would do just exactly that.
What should the response be to an attack by a bully? You can either submit and accept the beating, in the hope that someday the bully will weary of beating you up, or... you could (and should) respond quickly and surely, with all the strength you can muster. To accept the beating simply encourages the continuation of such behavior! A strong defensive response, on the other hand, has just the opposite effect - it discourages such displays of such aggressive behaviors. A swift and powerful response is what is demanded.
However......... there's another factor in the South Korea-DPRK situation. Apparently the "bully" from the North has the (thus far) unwavering backing of the Giant of the North - China - whose standing army is estimated at 2.5 MILLION (and, if you include paramilitary organizations the estimate jumps to 7.5 MILLION). To complicate matters even more, China has - primarily through lopsided international trade agreements - gained de facto control of the world economy.
Now you have to ask yourself, "If I defend myself against this little piss-ant, tin-horn dictator, will I also be fighting the hordes of Chinese military? How much affection does Hu Jintao of China really have for Kim Jong Il of the DPRK? Will we have any true allies if we respond and are faced with China? Will WalMart still be in business if China gets distracted for a few days?"
But, one thing is certain - taking no action is admitting you are powerless, and you will submit to the whims of your personal "bully". It escalates from bully to gang to army. International politics is a bitch... take the odds and kick Kim's butt!