How many atomic bombs will it take to destroy the United States?

This cannot be determined without knowing a lot more variables, including: yield per bomb, burst height/depth, "dirtiness" of the bombs (amount and type of fallout), weather.

It has been calculated that about 4 to 6 atomic bombs of about 3 to 10 megaton yield detonated high in the ionosphere at certain critical spots over the US at the same time would produce an EMP that would produce a surge in the power grid and also induce high currents in unshielded electronics equipment that would destroy all solid state electronics and severely damage most electrical equipment. This would certainly disable the US completely for some time leaving us open to other attacks that we would not be able to respond to. But it would not physically destroy the US.