Well, let’s look at this systematically —
The CIA apparently believes that North Korea possesses at leasttwo nuclear weapons. These are presumably atomic, rather than thermonuclear, weapons, which makes a pretty enormous difference in yield. Atomic bombs would not likely be much more powerful than the Hiroshima and Nagasaki bombs – i.e., something in the 10 to 20Kt range. A thermonuclear (“H-bomb”) warhead could be astronomically more powerful. Even figuring conservatively at a 1 to 2Mt yield, that’s 100+ times more powerful than an atomic weapon. By way of comparison, most modern US ICBMs carry multiple thermonuclear warheads of only 200-300kt yield each for reasons of efficiency, though single bombs of multi-megaton yield were common into the 1960s. While North Korea may well be working on developing thermonuclear capability, I know of noone who has asserted that they have it now.
Having assumed that they have decided to launch an atomic bomb at LA, lets also assume that it hits its target, and actually detonates. Estimates of the immediate death toll at Hiroshima vary pretty widely – anywhere from 40,000 to 130,000 people. Nagasaki apparently suffered only about half as many casualties, due to more rugged terrain, and possibly lower population density. While modern Los Angeles certainly has a much larger population than 1945 Hiroshima, it is also spread over a much larger area. Population density in the blast area could vary considerably just based on where, within the LA city limits, the bomb hit.
Consider also the superiority in modern transportation and trauma care, in a country that hasn’t been under intensive conventional bombardment for two years. Even though a nuclear blast would certainly overwhelm local, and seriously tax national medical resources, we’d be a lot better off than Japan in '45. For those reasons, it would greatly surprise me if the fatalities were greater than those at Hiroshima, and it’s quite possible they’d be somewhat lower.
Longer term cancer deaths would be very difficult to estimate. I’ve heard claims in the hundred thousands for Hiroshima and Nagasaki, but it’s difficult to find data from sources without an obvious agenda. I suspect that modern nuclearphobia would result in most people shunning the blast zone for many years, as was not the case in Japan, which would reduce the cancer toll somewhat. An offsetting possibility would be for the North Korean warhead to explode at or near ground level, unlike the airbursts over Hiroshima and Nagasaki. This would reduce immedate casualties by reducing the blast area, but would kick up more fallout.
I’d imagine a national panic over agricultural contamination (CA’s not so much the nation’s breadbasket as its fruit and vegetable basket, is it?). But the actual long term health effects would probably be less than feared (if only because the fears are so great).
Fatalities in the entertainment community could be negligable or heavy depending on the exact placement of ground zero. If a 10-20kt warhead hit downdown LA, I think the effects on Century City, Beverly Hills, and the major movie/TV studios would be slim to none (which isn’t to say there wouldn’t be panic, looting… think Earthquake). On the other hand, if the bomb fell on Century City, celebrity casualties could be fairly high, though 90% as a percentage would probably only apply within about a mile of the detonation (that’s about 3 square miles, out of about about 465 square miles and 3 million people in the city of Los Angeles proper – I’ll assume for now that the county has a lower population density than the wider county), requiring a near bullseye on 90210.
Effects on US military capability, other than the diversion of resources to disaster relief, would be nil.
The biggest unknown, I think, is the US response. I think it would be very much a function of how the situation had transpired prior to the attack. The knee-jerk assumption is that we would launch a missile back and flatten Pyongyang. However, I think the negative political consequences, and dubious strategic value, of such an action would make it unlikely. Surely you can all imagine the outcry against murdering innocent North Korean civilians in a pointless act of vengence. Instead, I would expect an immediate, all out conventional campaign to topple the current regime. As highly militarized as North Korea is, I can’t seriously believe that it would be able to defend for long against the full attentions of the US military. Subsequent nuclear strikes against the US would be highly unlikely, since I would expect North Korea’s ICBM launch facilities to be highly vulnerable to air attack. It’s possible that North Korea might expend any remaining nuclear weapons against South Korea, Japan, or even its own cities, once significant US troop strength had arrived, but I don’t believe that this would alter the final outcome.
The possibility that China might object to such an invasion raises the spectre of a broader war, but I think it would be politically difficult for them to take too strong a stand on the side of the government that just nuked LA. If anything, they might try to invade preemptively themselves, so as to be able to install a more tractable puppet.