As has been pointed out, interception is arguably best done (from a technical standpoint) during or just after boost phase, when the launch vehicle is a pretty unambiguous target. If the warhead bus has time to deploy countermeasures the job gets much tougher. During terminal phase atmospheric drag strips away the decoys and such, so target identification becomes a whole lot easier, but then you're faced with incoming at Mach 10 and only a short time until impact.
Previous answers have claimed that the available time to intercept is too short to do anything, so Democratica is hosed.
That, as it happens, is not entirely true. I present the early-70s answer to the problem, the Sprint missile
It uses explosive silo hatch bolts, a gas-piston ejection mechanism to get the bird in the air quickly, and accelerates at 100 g's to Mach 10 in 5 seconds.
Drawbacks? Oh yeah. The big one was the warhead, which was a radiation-enhanced fission jobber (read: neutron bomb). This is not entirely as bad as it might seem, since the high altitude of detonation means that there are no ground fires started, and nuclear winter is not much of an issue. Since the warhead is fairly small, "only" a few kilotons, fallout is not as bad as you might think.
Modern technology might or might not address the problem, since the last couple of decades has seen the development (and deployment) of kinetic-kill interceptors, which do the job by direct physical contact - no explosives, nuclear or otherwise, required. Of course, making a window to look for the target in a vehicle going that fast that low is not what you call a non-trivial exercise.
But it does serve as a starting point.