No conspiracy required - Or if one is required, then all the evidence indicates that it is openly in place, and is not seriously opposed by Congress.
From
Wikipedia:
The War Powers Resolution requires the President to notify Congress within 48 hours of committing armed forces to military action and forbids armed forces from remaining for more than 60 days, with a further 30-day withdrawal period, without a Congressional authorization for use of military force (AUMF) or a declaration of war by the United States.
Seems to me that the Generals are bound to obey an order to attack, unless they have:
1) Extraordinarily strong grounds to believe that the President has no intention of informing Congress; or
2) They have been attacking for 48 hours without such notification having occurred; or
3) They have been attacking for more than 60 days without Congressional approval and/or declaration of war
It would require a massive conspiracy of Generals to
defy an executive order to attack a foreign power, in the absence of at least one of these conditions.
It has been alleged that the War Powers Resolution has been violated in the past – for example, by President Bill Clinton in 1999, during the bombing campaign in Kosovo. Congress has disapproved all such incidents, but none has resulted in any successful legal actions being taken against the president for alleged violations.
So it appears that Generals have acted on Presidential orders to attack in the past, without waiting for Congress. Why would you imagine that they might refuse to act in the same way in a future scenario?