When Barr says he will not follow a court order after the case has been heard and appeals exhausted, then that would be a constitutional crisis- not going to happen.
Sorry but that would not be a constitutional crisis either. It would be the constitution working exactly as intended by the drafters. The three branches are co-equal. The judicial branch does not rule over the executive, despite the delusions of some federal judges.
It would hardly be unprecedented for a President to thumb his nose at a judicial ruling. If congress objects, they have the impeachment power, they have the confirmation power and they have the power of the purse.