I wouldn't characterize the capacity at all. Since the advent of nuclear weapons, our possession of them has made such a foreign invasion impossible.
Nor answer the question directly, with all due respect, and there is much.
I fail to see how a nuclear weapon would prevent a surreptitious attack through our demonstrably porous borders. We haven't made so much as a dent in the wholesale flow of contraband and undocumented individuals from the south.
I am not suggesting an unprofessional force to deal with the border, only pointing out our vulnerability, and the irrelevance of a nuclear deterrent in domestic defense.
We forget so quickly how a determined, creative enemy is capable of wreaking untold havoc in a single day. If 9/11 was only the start of an invasion, and not an isolated set of planned atrocities, we might be thinking a little differently about the role of armed citizens for immediate defense of communities. But our sense of invincibility is resilient, and illusory, in my opinion.
Certainly the professional forces are the real deterrent, but they are slow to mobilize. The people, on the other hand are everywhere. That, in part, is why I believe the founders considered the whole of people the militia.
I think we overlook the wisdom of that idea at our own peril. I am not ready to decide that the whole idea of the militia, or at least the capability of raising one, is useless and outdated.