Depends on who you are referring to. If I'm on the ground, I'm not tracking the situation in Washington as I'm too busy and there are too many between me and the President for me to worry about that. Again, as long as the orders are clearly not illegal.
If you are referring to the Unified Commander, such as the Commander of Africa Command or European Command, they do have a responsibility to ensure they have proper authority in place before ordering forces to engage. They will reference that authority in the operational orders they send out to the forces. If that authority is not clear they will and often do push back against the White House. We have troops in the Philippines and the Horn of Africa who cannot engage anyone except in situations of self defense despite initial Presidential desires for more active engagement.
If you are referring to the Chairman of the Joint Chiefs of Staff who sits as an adviser to the NSS, then he has a responsibility to inform the President of the President's responsibility to get congressional approval, as does the VEEP, SecDef, SecState, the Presidents Counsel etc. Congress has the responsibility to demand information and take action to approve or disapprove of the military operations. If the information isn't given or if the President pointedly ignores Congress, then they have the responsibility to impeach.