If you don't have health insurance, you have to pay for your own medical care. Eventually you will become "poor" by American standards but you'll still be wealthier than most of the people on earth, with a private, reasonably safe and comfortable place to live, a full set of appliances including a TV and a microwave oven, a car and the tools of your trade. Then you will be eligible for government assistance. You'll have to fill out a lot of forms and interview a dozen bureaucrats, and you'll be limited to patronizing doctors and hospitals that have chosen to participate in the government programs, but that includes somewhere between 25% and 50% of all the medical resources in the country so you won't have any trouble at all keeping up with your care. You'll be able to continue getting treatment while your applications are being processed and the doctors and hospitals will just wait to collect their money from the government.
Basically, no one in America is allowed to die from an illness because they're poor. If you're found lying unconscious on the sidewalk the police will send an ambulance to take you to a hospital, and the people in the hospital accounting office will be stuck with the problem of figuring out who's going to pay for you. They may track down your estranged mother or your ex-spouse, but they won't delay your treatment while they're searching.
The only poor people who die from lack of care are the crazies. It's very difficult under our legal system to force people to accept medical care if they refuse it.
Yes, people die of AIDS every day in America, but that's because there is still no cure for it, not because they're broke. It's particularly bad in some of the ethnic minority communities where people don't have the tradition of speaking candidly about sex like we do, and where condom use is so much lower.