"Can the President grant immunity from prosecution?":

I love Fox's 24. A common plot device in the show is for the bad guy to demand and get a letter of immunity from prosecution signed by the President in exchange for some vital piece of information. The immunity always seems to hinge on the information being true and resulting in the capture of some villain or the recovery of the explosive du jour. Is any of this true? Can one demand immunity from prosecution signed by the President, and, more importantly, can one expect to get it?