I sew bindings on professionally. 2" is the narrowest I've done, and it was a little challenging. I sewed the binding on by machine, then turned to the back to sew by hand as usual. Found myself putting the needle in right at the stitching line I'd just made to sew the binding on the front. It was a pain. If you do use a 2" binding, I suggest using a slightly smaller seam allowance when you stitch the binding on the front. As others have suggested, a flange binding would be easier and very attractive.