There are systems in place (a sea-based one in Japan and some land based ones on America's coastline) but a complex attack with a reasonable number of decoys could probably slip at least one missile through. The more immediate threats are against Japan and South Korea, though.
In large part because the DPRKs don't really have a proper launch platform capable of reaching America. Warheads are heavy things, and even North Korea's attempt at a space program demonstrated the targeting issue is nowhere near resolved. ^_^
At any rate, a nuclear missile that gets shot down in the atmosphere is a dirty bomb, nothing more. Nuclear warheads are very touchy, very finely-engineered pieces of work. If the shaped charges don't blow up just right, frequently, all they'll do is scatter very radioactive material over a wide area, but nowhere near the amount of damage or radioactive output that a proper explosion from a nuclear reaction (either fission or fusion) will accomplish. In other words, it'll be liable to do even less than the old stratospheric testing in the 1950s. The worst that might happen is that chunks of radioactive debris might get scattered all over the place, but such problems would be localized to the impact sites. The real issue is getting to the point where it can be shot down reliably; American ABMs (the Patriot missiles) hasn't exactly proven itself wonderfully against even conventional ballistic missiles, though it is getting much better than it was in, say, the first Gulf War.