I have run into several 66s where the presser foot shaft was adjusted way to high and it didn't fully contact the needle plate.
Remove the face plate. Lower the feed dogs, unscrew the pressure adjuster from the top of the presser foot shaft. Then lower the foot and very carefully loosen the set screw that holds the presser foot shaft lifter part.
Gently work the shaft down till it rests on the needle plate making sure the sides of the foot and the feed dogs are parallel. Then snug up the screw. Test the adjustment. You should have around 5/16" ± of clearance between the bottom of the foot and the needle plate with the foot raised.
Also make sure there is some clearance between the presser foot lift lever and the part it moves when the foot is down. You don't want a "0" clearance there.
That should do it. There are adjustment specs in the manuals. I'd suggest you find the right one in the Singer site and download it. I do not have a list of which link goes to what. I gotta do that someday.
Joe