Well, the simple solution is you destroy the American Navy and Air force. Our current missile arsenal isn't actually all that large. Our 68 burkes for example could hold some 96 missiles each or about 6,500 missiles. However, the modern anti air missile you would assumeldy want to stock those with has only had about
500 of those missile built. Tomahawk missile stock seems to be in the realm of a few hundred, with something like 100 built per year.
So, you invade the US by destroying the Navy. So, slow grinding until the Navy and air force are attritioned away assuming your not allowed to just build up a massive army on the boarders capable of grinding the US military down in fairly short order.