Cheri, I also have the Singer Quantum 9960 and don't have a problem sewing through layers.
In fact, when I made this tote, I straight stitched through 2 layers of fabric, a layer of batting
and a layer of very stiff fusible interfacing.
After I was about half way done I realized I had even forgotten to put my walking foot on.
No problems whatsoever and very nice stitching. Crooked lines due to user error
I do believe it's your machine.

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