Photoshop has no easy way to do this. Turning the image into a brush will make it black and white. Not what you want. Turning it into a pattern stamp will repeat it at fixed intervals into a tiling image, not so much with the "smeared"/repeated effect you're going for. Duplicating the object repeatedly is (in my opinion) tedious.
Essentially you're looking to duplicate the image along an arbitrary path.
It would be much easier to use a different piece of software that can do full color "brushes", such as Paint Shop Pro. In Paint Shop Pro, the feature is called Picture Tubes. It allows you to mask an arbitrary image and use that like a full color brush.
Corel has a couple of nice tutorials on their website on how to use it: http://www.corel.com/static/product_content/css/discovery_center/tutorials_pdf/photo/PictureTubesInPSPX4.pdf
From the first tutorial:
...As you paint with the Picture Tube tool, Corel PaintShop Pro X4 paints one image from the picture tube after another. Many picture tubes create separate, discrete images, and others create the effect of a continuous image...
You will want to set the step parameter very small to get the effect you are after.
Adobe Illustrator apparently can also do a similar effect. But my suggestion is essentially "try a different program" if you want to repeat the image easily.