What does Firefox have to do with it?
I can see why it would jitter. The distance the Sprite moves each frame will vary with dt, and since the "push out" action works something like the following I could see why some frames the Sprite would move and some it wouldn't.
While
Sprite overlaps solid
--- move backward 1 pixel
There are two reasons why box2d doesn't jitter. The first is it uses a fixed timestep, and secondly it calculates how far to push out.
You probably could do either and eliminate the jitter.