My Grandma Gean was a firm believer in this. She made a few extra dollars by sewing for people in the neighborhood, everything from quilts to underwear. One year on January 1st, she was behind on her sewing and needed to get some things done, and she disregarded the superstition. Not long afterwards, she was called on to sew a burial gown for a stillborn baby girl. That did it for her; she never sewed another stitch on New Year's day.
I'm 99% sure that this superstition holds no power; but there is the Chaos theory, and just in case, just if, maybe it will work for us this year.
Time will tell.