Assuming that "us" means "the USA and whoever else wants to come with them," then My prediction is that the war will (not would) take around two weeks with very little post war mess. America has been planning this war for the past decade and our advantage is we have been able to see how a slightly similar war and the stategies used in it worked. Then again, we'll see.

Iraq was as flat as the desk I'm typing on, yet the entire Korean peninsula is hilly and mountainous, no less so for North Korea. Therefore, military hardware may be slower to advance. However, with satellite data at MY fingertips (and the fingertips of any common citizen with Google Earth), US intelligence can rely on them to figure out the fastest paths and what to destroy in these paths. Though the land advance may be a bit slower due to the terrain, there are always precision armaments at our disposal, plus remote-controlled drone fighters that will take down hilltop defenses and take care of advancing enemy troops well in advance. There will also be forward sea landings, which will send the average invasion speed rising again, so Pyongyang may fall in ~2 weeks, then the northernmost parts of the country in 1 month.

Well, here is my guess from a friend: North Korea Vs. South Korea Coming Soon. -The start of the 2nd Korean war- 1) North and South Korea begin a short period of a 'war of words' 2) Both sides begin to move massive numbers of men and material up to the front 3) Led by the U.S. President, the Western world swings in solidly behind South Korea, and the U.S. begins to move additional military units to South Korea. 4) After proper posturing, North Korea attacks. After penetrating some short distance, North Korean troops begin to be destroyed as American troops, equipped with the same lopsided margin of capability as we had against Saddam Hussein, rapidly kill North Koreans by the tens of thousands. 5) In desperation, North Korea then launches a limited number of nuclear weapons or threatens to do so. 6) America rapidly comes to the aid of South Korea, rushing in nuclear capability 7) China, likewise, backs North Korea 8) Now, the confrontation is between China and America, both threatening each other with nuclear annihilation. The world panics ---------------------------- At the same time, in the Middle East, Israel is annihilating her Arab protagonists, setting the stage for the planned appearance of Antichrist. The world panics ------------- At the same time, Arab terrorists strike American and European cities with wide-spread terrorism, and threatening to use nuclear devices. The world panics ---------------- At the same time, riots erupt in American cities. America panics ---------------------- Maybe the Stock Market goes into a free fall, reacting badly to the out-of-control events. The world panics So it will last a long time.

the answer depends on who "us" is. Who is "us"?