2D Screen Overlay with Looping Texture

Hey,

I'd like to make a screen overlay for a 2D game, simply a texture that covers the whole camera/screen and can infinitely loop/scroll at given X/Y directions. In my case a mist texture.

Here's a good ref for what I am aiming for:

What i have now is a plane with a texture where I change the texture offset, this doesn't work for GUITextures though. Problem with using a plane and material is to cover the whole screen, if I do it by scale the texture gets scaled as well which is not ideal.

How about using Tiled Texture for repeating if I don't want to use a big texture to cover the screen?

I am not sure what's the best way to handle this but if anyone can point out a good solution or practice, please do.

Thanks!