You MUST MUST MUST lower the presser foot - even if it isn't there. Otherwise, there is no 'squeeze on the upper thread in the upper tension disc. I'll bet my booties you think it is your bobbin thread, but it is the top thread looping on the bottom. Use 2 different colors - and you'll prove it to yourself...forever!
Well, try this: NO presser foot =- but but but be SURE to lower your presser foot anyway - because only when you do that, is the upper tension 'engaged'. You might even have to take off the ankle that holds the presser foot.
Then - guide it all through yourself...with your tongue held just right..... with one hand in back, one in front. You'll probably break some needles -
I did this to 'couch' on some rhinestone trim just 2 days ago - worth a try...
I think you are asking how to sew close - real close - to the bulk of the cord. You have to use a zipper foot - and probably employ the use of changing where your needle 'rides' on your sewing machine. Some machines have 'needle position' - which moves the needle from left to right, instead of it riding in the center of the h*** in the needle plate. On other, simpler machines - you can adjust this on straight stitch with the stitch width knob. You might have to (oh my...) look it up in your manual. This is very common with the bulk of the coil of a zipper. The foot will ride opposite of the bulk of the cord, and the needle needs to ride as close up to the cord as possible. Worst case scenario, that four letter word - stitch it by HAND with a back stitch.