We already have several developed, deployed, and tested ABM systems (Patriot, THAAD, SM-3, and the Alaska-based exoatmospheric interceptor missiles whose program name escapes me at the moment) which can deal successfully with a limited numbers raid like the one you postulate.
The recent successful ABM tests conducted by the Missile Defense Agency (MDA) were, among other objectives, meant to underscore the existence of this capability to outside parties, especially hostile ones like North Korea and Iran.
Along with the MDA, a big thank you is owed to President Reagan and all subsequent presidents (both Democratic and Republican) and Congresses for their support in developing this capability. It took a long time and a lot of money to accomplish it.
This is why the question of what to do once you have defeated a limited nuclear ballistic missile attack is salient and why I think the Chinese would act pre-emptively. They don’t want to find out how well or poorly their ABM defenses would perform when dozens of US nuclear missiles in multiple waves come arcing over the Pacific inbound for North Korea.
The current crop of deployed anti-missiles, and those projected for the near future are 50% effective, even under prepared and forewarned test conditions.
I am not ready to protect my home with a security system that alarms 50% of the time, nor a weapon that fires 50% of the time I pull the trigger, and being that you are a smart FReeper, I doubt you are either.
Be well.