Nonsense

First, you should be looking for another job anyway. A good workplace doesn't do that, and you should look for one.

Second, if they could afford firing you, you wouldn't be overloaded with more work than you can handle.

Third, go fight for some adequate health-care that is independent from your workplace. The way the US (and yeah, it's only the US) does it is borderline a human rights violation. At least officially, you live in a democracy, so go demand it works for you.