Why not just allow them to put a green tag on your bag and then take it on the plane anyway? (The GA doesn't follow you down the jetbridge...) I often do this with a Wenger rolling computer bag, which does not look as if it will fit in the overhead of a CR2 or an RJ145, but will in fact fit perfectly well if you put it in head first with the wheels facing out. That doesn't work for standard rollerboards, though.
Bingo!
Just be cool, let them tag your bag, and smile while keeping your lips sealed, Then mosey on the plane, palming the greenie!
If it absolutely doesn't fit, or you can't find a bin large enough, put the tag back on and set it out by the door!
Problem solved --- as 1P so rightfully indicates!
You could be having a cool one during the time your trying to win a battle with a stubborn g/a, who is enforcing some arcaric rule!