Uh yeah I definitely sit with one eyeball physically touching the screen, and just pan around if, for example, I need to see the score on a basketball (go Lakers!) game. It gets me into the action, and the "eye saliva", as I like to call it, makes sliding across the screen a breeze. Try it sometime (but try not to get hurt, because plasmas like mine heat up the eye pretty quickly and your eye saliva starts to boil).
I actually just press my nose up against the set. I call it "As close as you can get to HD without actually getting wet."
2 feet or under, really? You can't even see the whole screen at that distance (well, with my 61-inch you can't).