You really shouldn't use the tiled background object for filling the screen with a single color.
You should either of the following:
use the background parameter (in layer properties) to fill the screen with the color you want
create a layer that doesn't scroll (don't remember how exactly, might have something to do with parallax settings (0?)), have a 1x1 pixel image of the color you want added to it, then stretch it to your screen size (point sampling might give you better results)
And contrary to the beliefs of the guys here, i'd say that you should go with slicing up your image into smaller parts, here's why:
i read on one of the threads you can find here that the objects that are off-screen are not drawn, therefore don't take up some of the time needed for rendering a frame (however the images are still in memory, so there's that), which means that if only a certain part of your whole level will be visible at a time, the images that are off-screen won't take up the systems' resources and you should, in theory, have better performance than if you just used a single huge image. Or something... /speculation
Using a plain color background would still be faster than using a sprite... :/
If you'd like to know more about the performance optimization, i made a thread recently, where i asked for feedback from others on my views, but it appears that it's gotten buried now.
Here it is: scirra.com/forum/optimizing-a-game-for-mobile-platforms-your-tips_topic78778.html