As an officer, you swear an oath to the constitution, not the president. Now, the phrase “not in the best interest of the United States” is subject to a lot of interpretation, but if it really meant “unconstitutional”, then the JCS generals were spot-on.
If it meant “contrary to the generals’ wishes”, it was mutiny in the planning.
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.