We've had bad things happen on the internet so many times that we're pretty much immune to them now.
There is a huge difference between taking, say, whitehouse.gov or army.mil down verse our real command and control networks--which are probably next to impossible to take down considering there are layers upon layers of backup communication systems.
The idea of a "cyber-attack" being used as a first salvo in an act of war against the United States by any nation-state is pretty ludicrous, as it would minimally (if at all) affect our ability to destroy whoever was dumb enough to try it.
It would be something more Pearl Harborish, like a nuke or EMP detonated in space over the US that fries our communication networks and power grid.
In which case, this proposed kill switch would be redundant.
A high altitude nuclear detonation above the continental US is the first strike protocol for any nation-state that would try to attack us. Even then, a lot of our military's core command and control infrastructure has been hardened to withstand such an EMP for decades--as it was known that a high altitude detonation over US soil was the Soviet's plan for a first strike...That is why Cuba was such a big deal. Still, the EMP would completely decimate every non-hardened electrical system.