Can I be force to resign if I will not be able to work due to my illness?

I recently was diagnosed by my doctor for high blood pressure he placed me on medication and told me to come back for a follow up visit. My work performance has changed due to constant headaches and trouble focusing. Prior to going on I notice I had a really bad cough causing me to not sleep but it was noticeable before going on medication. I work in a call center so I would have cough spasms now and then and it would go away but it has gotten worst my doctor states it might be an infection and he placed me on some antibiotics. Now I called and texted my supervisor to advise him of the situation and that I will not be able to come in for a whole week. He never responded so I called him and he advised me that his boss said I should resign. I could not believe this I mean here I am wanting to get leave of absence so I do not bring any of my germs and also to make sure I'm capable of getting my health together and this is what things are going to boil down to be. I'm very much disappointed. I then advised my supervisor that I cannot resign and it is either you guys fire me or lay me off because I have a family and my health is going down the drain. I told him I have a note from my doctor clearly stating that I will not be able to work due to my illness and they do not get it. So now I am waiting for a response but now I'm very skeptical about going back because I might go in and they fire me anyways. I need to know can a job force me to resign and what are my options other than quitting. Thanks.