All the  assets for this project can be found here:

Scrolling Background

We want to make this static background... 

scroll infinitely!

I have set my display properties like this

The background for our level is a TextureRect

We set the Stretch mode to Tile

Use any of these images as the Texture

Tile the image across the screen

Setup your scene tree like this:

TextureRect Properties

Tile your TextureRect like this: