Jane, when I do granny squares, I don't sew them together (though a whip stitch matching stitch for stitch is pretty fast), I crochet them. I use either slip stitch or single crochet while holding the two squares right sides together. When I get the first two of the row done, then I do the next two without breaking off the yarn - like chain piecing quilt squares, if you're familiar with that process.
Eventually I have all the rows crocheted together, then I crochet along the columns, criss-crossing the previous "seams" whatever way seems to work best for that particular project. Hope that makes it seem less daunting to tackle :) I admit to loving granny squares and I'm glad they're back in fashion, at least for a little while! Holly