I have an old singer that takes a "different" needle. It is a shorter needle than the "regular " needles carried just about anywhere. I can find them on line. My machine takes a singer 206 needle. Schmetz does make that needle but you need to know how to convert to the Schmetz sizing ( they make hundreds of different needles).
There was a time I too thought I was out of luck if my last needle broke or got dull. It will take a bit of work but you can get needles.
First make sure your machine really requires a specific special needle. When was the machine built? If you have any issues a good Sew and Vac or reputable repair person can help you find /source your needles ( if it is required).
Just a note : universal needles do not refer to the machines it will fit, it is refering to the fabrics it can be used on. A universal needle is for sewing on knits as well as cottons. The point is not the same as a needle intended for quilting. For general sewing they are just OK... buying the proper needles for specific fabrics can make a noticable difference in some stitches.
You may want to give this source a call
http://www.sewingpartsonline.com/sea...d=Kenmore+1782
http://www.sewingpartsonline.com/sea...x?find=Kenmore