The width of the backdrop is 20 ft. It will be projected onto a wall. What size should the photoshop dimensions and the resolution be? This is not going to be a print file, it is going to be displayed digitally!
Simple. See the specs for your projector.
If it is a FullHD (1920x1080px), make your file FullHD.
If it is only HD (1,280x720px) make your image HD.
It does not matter if the image projected is 1 ft or 20, or the distance to the wall. It does not change the fact that your projector can only project at its native resolution.