That's the worst part of it. The warm up is only the first 10 minutes or so of class. Anyone should be able to push themselves for 10 minutes or so. I love the style, and the club atmosphere, and wouldn't want to change it even if I had the option (small town, not many clubs). If I can just get to a basic level of fitness, I'll be fine. I'm playing catch-up though after months of illness. Imagine if for most of a year you could barely even help out at home with the routine domestic chores. Nearly a year of doing even less than than most lazy people. That's me. That's what I have to work with. Somehow I have to achieve a basic level of fitness as quickly as I can without killing myself, so that I can go to class without having to worry about having to raise the hand of shame (ie put your hand up to declare that you're out).
No -- not everyone can push themselves super hard for 10 minutes, especially from a cold start. On top of that, you're still recovering from a pretty massive insult to your body, based on your posts.
Again, I'm going to suggest seeking guidance from a qualified personal trainer. They'll help you get back in shape, and keep you honest -- while giving you an honest assessment of where you stand.