We have a working tabletop Singer JA606949 sewing machine. Just sort of became curious as to what the rarity of these things are? Is it of any value?

Here is a picture of the machine

I have seen a few of these at auction. These were not the best Singers ever made, and were not made in the U.S. With perfect adjustments it may sew pretty fair, but it will never compete with the U.S.-made models (i.e. the 201 or 500-series). At auction, it might go for $15 to $60, but worth depends upon what someone is willing to spend.