The normal course of events for a person who defies a court order is that the court would issue a warrant for their arrest for contempt. This warrant would then be executed by the relevant law enforcement agency (US Marshals, FBI, local police, whatever) and the person would be placed in jail until they agreed to comply with the order.
In the case of an organisation that was refusing to comply, arrest warrants could be issued against each person who was not complying until someone decided that they would comply.
In practice, a government agency would either immediately comply with the order or lodge an application for injunctive relief from it in a higher court.
Of course, if everybody refuses to comply with a court order you have what is known as a breakdown of law and order and things get really, really bad e.g. Syria.