Alright time to set some stuff straight
the United States has probably the best national missile defense program in the world. However, this system is not designed to stop all incoming missiles. In fact, the launchers and laser systems are based almost entirely around major cities and military bases, and meant to minimize damage from a strategic first strike.
The North Korean military is lagging behind western standards by about 20 years, and that's the CIA's best guess atm. Any invasion made by north korea into the south would be almost immediately repulsed, with the counterattack probably resembling the korean war all over again. That is where this possible WW3 could come about, not from north korea but the political fallout of a nation committing economic and diplomatic Self Delete.
edit: and then china entering the war under the pretense of protecting her borders. After that it would just be a matter of everyone taking sides.
Obama hasn't killed any programs or funding to the military. Congress controls the national budget, take it up with them. IIRC Obama has actually tried increasing funding before but I don't remember where I read that.
WW3 would likely leave us in an advantageous position to the one we have now. A war with a clear-cut, defined enemy (none of this al-queda mountain man bullstuff) would generate manufacturing jobs and probably kickstart the economy (see: world war 2).
I don't know why everyone is so convinced the missile failed. I haven't seen any footage of the launch and subsequent destruction, but has anyone taken into consideration that there is at least one patriot missile battery deployed in south korea? It would not surprise me in the least if the US shot it down as a propaganda victory for the west, and turned around and claimed North Korean ineptitude led to its failure.