[Jtsummers]

The military drills into its officers and enlisted personnel the fact that they not only can disobey an unlawful order, it's their duty. A direct presidential order is not inherently lawful, and I'd expect most commanders (especially, in contrast to lower ranking enlisted or officers) to be able to respond appropriately.

[dragonwriter]

Even granting your position for the sake of argument, while the set of “orders to use nuclear weapons that the public would, in retrospect, consider catastrophically undesirable” and that of “orders to use nuclear weapons that would be clearly illegal” might overlap, the former is clearly not fully contained in the latter.

But I’m not sure we can take your position as true, anyway:

First, the historic lack of accountability for illegal Presidential orders or obedience to them both reduces the clarity (through absence of case examples) of the legality of such orders and reduces, due to incentive structures, the probability of any person choosing to be the one that takes a stand on the perceived illegality of such an order even were the legality relatively clear.

Also, given the War Powers Act, its not clear how any order to employ the military by the President (except domestically in a manner violating the Posse Comitatus Act) would be illegal under domestic law initially (which, for a nuclear attack, is all that is going to matter.) It might violate norms of international law like waging a war of aggression, but I think recent history shows that even if maybe you can trust the US military to resist some set of illegal orders, “orders to wage of war of aggression that is, nonetheless, authorized by US domestic law” is pretty clearly not within the scope of “illegal orders” for which that is true.

[jki275]

There's a bit of nuance to this.

An order is presumed to be lawful under military law. The burden of proving it unlawful rests on the person receiving the order. The default is to execute the orders given.

In the absence of some direct reason that it would be unlawful, a military person must carry out the order they are given.

Now of course, as you say, it is the duty of the one ordered to do something that is unlawful to refuse to carry out that order.

[dragonwriter]

Even granting your position, but while the set of “orders to use nuclear weapons that the public would, in retrospect, consider catastrophically undesirable” and that of “orders to use nuclear weapons that would be clearly illegal” do overlap, the former is not at all fully contained in the latter.