4096 isn't supported on some devices. Modern iOS devices (except iPad mini) support it, but a LOT of android ones dont.
If its just for a background, why don't you just use tk2d > Sprite From Texture, as its available in 2D Toolkit 2.0? You can simply import your background texture directly into it - you'll have to make it non power of two and disable mipmaps, but that should be it.
With performance, you're probably doing something that the GPU doesn't like, like drawign too many transparent layers on top of one another... If your background is solid, make sure to use a solid shader. tk2d/SolidVertexColor. That will help massively.