Disclaimer: I find Sarah Palin's views on foreign or military policy appalling and am not defending them here. My point is a simple one about the logic of this exchange, not its policy content.
As I have pointed out before, Obama has a curious penchant for obviously fallacious reasoning. Here, if you scroll to 35, you will see a textbook-worthy use of argumentum ad hominem. The Obama administration has recently released a "nuclear posture review" that promises never to use nuclear weapons against non-nuclear powers who adhere to the non-proliferation treaty. Palin claims that pledging you will not use weapons in your possession is a strategy that weakens your defenses against aggression, like a kid on a playground who pledges not to hit back if struck.
Obama could have responded to this seemingly inevitable objection with one of the available counterarguments (a couple of which seem obvious to me). Instead, with smirking contempt, he belittles the source and says, in effect, that nothing she says on this subject could be possibly deserve a logical, factually-based reply.
This merely illustrates something I have said before. Obama's fallacies are not mere non sequiturs. He tends toward ones in which he attacks an opponent in ways that are unfair or disrespectful. (See above link.) This man's addiction to fallacious reasoning is not an intellectual failing at all. It is a moral one.
BTW, getting a little closer to the substantive policy issue, a better version of the Palin objection was that given yesterday by John Derbyshire:
Last week the administration put out its Nuclear Posture Review, telling the whole world the circumstances under which we will use nuclear weapons, so long as we still have them. This misses the point that the whole purpose of nuclear weapons is to make one's enemies nervous, not knowing whether you'd use them or not. Will we go nuclear if China invades Taiwan? Will we go nuclear if Iran attacks Israel? Will we go nuclear if Russia marches back into Estonia? How about if some terrorist lets off a nuke in Seattle and we trace it to North Korea? When, where, and how will we go nuclear? Let 'em guess!