The few Kenmores I have with tables have separate model numbers for the table itself, which may be the 66.127 you reference.
If you lift up the machine out of the table, just under the base running along the front edge, is there a stamped metal plate with a number XXX.XXXX or something like that? If so check towards the bottom of this page
http://www.doubleveil.net/zssmp/resources.htm
and see if you can find a model number. The newest Kenmore I had was a Model 52 but had a different number on the stamped plate I am referring to. You may be able to use the XXX.XXXX number in a site such as sewingpartsonline.com to come up with the Model number. If you figure out a model number then try manualslib.com to search for either a Sears XX or Kenmore XX.