On a practical level, in over 18 years of law enforcement experience covering courts, jail, patrol, riots (Remember Rodney?), and natural disasters, I have never nor have I ever heard of anyone deputizing a private citizen.

An interesting sidenote is Calif. Code of Civil Procedure section 211:
"When a court has no prospective jurors remaining available for voir dire from panels furnished by the jury commissioner...the court may direct the Sheriff to summon, serve, and immediately attach the person of a sufficient number of citizens having the qualifications of jurors, to complete the panel."