Bureau of Prisons set deadline for Navarro's detention in Miami pending Supreme Court intervention.
Chief Justice Roberts supports lower court decision against Navarro's request to remain free.
Navarro convicted for refusal to cooperate with House committee probing Jan. 6 Capitol attack.
Navarro's claim of executive privilege unsupported by evidence, says U.S. District Judge Mehta.
D.C. Circuit Court rules Navarro forfeited chance to argue executive privilege, unlikely to win appeal.
Justice Department rebuffs Navarro's argument, emphasizes committee's need for information.
Jan. 6 committee seeks Navarro's testimony over his book's election scheme revelation.