Each individual must make that decision whether they are a general or not. The point is that we still have civilian control over the military. If the JCS had a formal agreement to make them the ones to decide whether to carry out the orders of the President or not, they are in violation of the Constitution. They could resign rather than carry out the order, but to actively disobey it and stop that order from being carried out is a far different matter.
I disagree. At that level, one's resignation must be approved or disapproved by the very person who is being disobeyed.
Further, if a commander judges an order to be illegal or immoral, it is that commander's responsibility to ensure that soldiers in their command do not follow the illegal/immoral order. At the JCS level, that means countermanding the order for the entire services.
Finally, the generals swore an oath to uphold and defend the constitution of the United States. Under nearly all circumstances, that means taking orders from the President and his civilian leadership team. Under extraordinary circumstances, where the civilian leadership has breached the constitution and its subservient laws, it means NOT obeying the President. If the generals had sworn fealty to the President, or even to the office of the President, then their duty under the oath would be obedience to the order. If they swore loyalty to the President, they would in effect be a private army at the disposal of a politician, rather than an arm of United States policy under the direction of the duly elected leader of the country.
Just my opinion, of course. And may God grant that we (as a country) never have to see such extraordinary circumstances as would cause the military to forswear the orders of a duly elected President.