The meaning is that you are going to go out and get smashed, off your head, wasted, proper pissed. When someone says Im on a Nixon tonight it means they are going to go on a proper bender, Only the strongest can survive going on a Nixon. You have to be a proper party animal to be able to handle it.
When one is said to 'pull a Nixon', it means that s/he was in a position of power, until screwing up really bad. Facing the consequence of firing/impeachment/whatever, this person resigns to avoid this punishment, as Nixon did.
When introduced for a speech for which you are unprepared, you extend both arms and hands, fingers making the peace sign. A plan can be formed during the resulting applause. Former US president Nixon's famous gesture.
Jerry decided that pulling a Nixon when he was given that award at the benefit would be useful. He figured out his whole speech during the applause.