Is it death? Seriously, it could be. You need to become serious about this. I know from ghastly experience that infected tonsils can cause a number of other issues, including affecting your heart and causing many serious systemic health problems including possibly sepsis and death. From the sound of this, the employer is hearing "tonsils" and not taking this surgery seriously. I had my tonsils removed when I was in my 20's and got very little sympathy or cooperation from my employer, even though it was very necessary for my continuing health. "Tonsils, tonsils, why didn't you do that when you were a child?!"
If I am reading this right, it is a store, it is being suggested that you not do the surgery the whole month of December, because of their staffing issues, and that's pretty absurd. The employer will have to give you FMLA, I think we have determined that, right cbg?
I believe I'd present my employer with a note from my physician that my surgery was medically necessary. And then just say, "I've got the surgery already scheduled, will be back......" and let them deal with it. I have heard many supervisors play this one on employees, especially diligent, good employees. It is NOT YOUR PROBLEM to make sure that shifts are covered, or that your supervisor is out that month, or whatever excuse the man is offering you why you can't take care of your health. This is about you and your well being, and you have as much right to be out and to have surgery that is very necessary to your health as your supervisor has to be out for whatever reason. I sort of doubt if the employer will fire you under these circumstances. Good luck with your tonsil surgery, I hope it makes you feel as much better as mine did.