That was Runaway Jury. In the book by John Grisham the guy got himself onto the jury of a tobacco lawsuit. Of course, the idea that you could get yourself into the jury pool and manage to get selected for jury duty the very day that the jury pool for a particular case is being empaneled is pretty far-fetched.
The right amount of dead presidents in a plain brown envelope handed to the clerk that handles jury pools is not at all far fetched.