[ATTACH=CONFIG]318056[/ATTACH] Thought I'd try it. Right after I posted the link here, I realized that I already had a handy gridded ironing pad, some fusible interfacing(old, and I'm not sure it's the lightest weight) and a supply of 2" squares with no purpose in mind for them. It took me about an hour to make this piece which could become an ugly mug rug, but mostly served as a means of testing this technique. I think it was faster than sewing strips and it's easy to be quite accurate. It's ideal for using 2" squares that are already cut, where the strip piecing technique could not be used. The fusible stiffens the fabric some, but depending on what you're going to do with it, that might not be a problem.
As I was working I realized that I could have kept going beyond the size of my mat by ironing only halfway across the last row and then moving it over and adding more rows. My mat was only wide enough for 5 squares, so I tested that and it works. If you want to go further than the width of your interfacing, you could also butt the next piece of fusible about midway through a row. It's not impossible, in other words, to do a huge quilt all in little squares using this technique.
Another thought that crossed my mind is that it may be possible to use freezer paper instead of fusible web and remove it as you would in paper foundation piecing. This would - if it works - take care of my only objection, which is the extra stiffness. I like to make doll quilts, and the stiffness would be more noticeable in a small piece. It might not be a problem at all in a potholder, table mat or mug rug.
If you make one, I hope you'll show us. Elizabeth Hartman of Oh, Fransson! gets credit for the tutorial.