The OP's desire is to have the image straddle the visual edge of the container; padding may be needed for other things, but won't accomplish that.
The best way I can think of to have a bg image extend over a visual edge is to have that edge belong to an outer container, and use negative margins on the inner container to pull its bg image to the desired position. Note that this may not work if one of the containers is a table cell - I have found that they don't obey some styling properties that divs obey.