By now everyone's probably heard that North Korea's probably got their nuclear weapons small enough to fit on an ICBM; https://www.washingtonpost.com/world/national-security/north-korea-now-making-missile-ready-nuclear-weapons-us-analysts-say/2017/08/08/e14b882a-7b6b-11e7-9d08-b79f191668ed_story.html?utm_term=.9e27bcd93746
That article gives an upper bound of 60 warheads (most other sources I've seen are lower, around 20-25). That's more than one for every state! Is America in existential danger?
The answer is no, not exactly. 60 warheads is nothing compared to our own arsenal, or what the Soviets had pointed at us back in the day. Assuming each warhead kills 200,000 people (probably an overestimate, North Korea has not yet developed hydrogen bombs, and they are probably reserving a significant amount of their warhead for use against South Korea / Japan / ground forces on the Korean Peninsula) that's 12 million deaths. That would be by far the worst tragedy in American history, and would have massive effects on society as a whole, but it is only a small percentage of our population (ballpark 4%). France about the suffered the same proportion of casualties in World War 1 and won, while Paraguay lost 70% of its male population in the War of the Triple Alliance and still exists nowadays (albeit with less territory than before).
Now that I'm done channeling my inner LeMay, what exactly can we do about North Korean missiles? I'm going to discount a preemptive strike; finding road mobile missiles is hard as shit, and any attempt to do that would almost certainly result in a war that leaves thousands if not millions of Koreans, Japanese, Americans, and others dead (this is bad).
Here's a great circle route from Wonsan (city on North Korea's east coast) to Albany, one of the farthest northeast targets likely to be hit.
(being an asshole, Kim Jong Un will not use one of his warheads to cure America of Patriots fans once and for all)
And here's a route from Wonsan to San Diego, about as far southwest as you can get in CONUS.
(interestingly enough, the difference in range is only about 700 miles or so)
You'll notice that both trajectories fly pretty near Alaska (most trajectories to the middle of the US will actually overfly the state). Clearly, if we want to intercept North Korean missiles, that's where we should put our defences. Boost phase interception is logistically tricky and relies on parking your weapon system right near a nuclear armed country. Terminal phase interception requires you to put a whole bunch of interceptors near any likely target, which just isn't worth it for 60 (probably more like 10) missiles.
The US military, not being entirely run by morons, has put their existing missile defenses in Alaska already; https://en.wikipedia.org/wiki/Ground-Based_Midcourse_Defense
However, that system has had a mixed record in tests. However, it is getting better, and it probably our best option in the near term for defense against missiles.
You can make the problem easier by not requiring a direct hit on the North Korean missile to kill it. Now, instead of having to hit a target travelling at hypersonic speeds with another chunk of metal at hypersonic speeds, you can just get sort of near it. We had that problem solved back in the 70s (though a modern version would need a bit more range to cover all trajectories at midcourse). Of course, detonating 5 megaton warheads in the upper atmosphere opens up a whole political can of worms and other issues and makes people unhappy and oh god it's such a pain. Good luck dealing with that.