As many have pointed out, a person who chose to be taken to the hospital would be taken to the hospital and treated whether they could pay for it or not. The result of this would be a serious amount of debt, but likely could be paid down with a monthly payment. The worst case scenario is bankruptcy, which sucks (though it sucks much less if you're already poor and have no credit to destroy). Best case scenario, is that you make a lot of sacrifices, cope with making the monthly payments for many years, and eventually become debt free again. Like I said: best case scenario.
I think that anyone would agree, though, that either outcome is far better than dying young. (Also note that none of these scenarios includes going to prison for failure to pay your debts. There is no such thing in the U.S. legal system, except for certain debts owed to the U.S. government, and even this situation is rare and typically involves willful failure to pay, not mere inability. Private debts are just that: private.)
The real problem is that people in the U.S. are forced to make this sort of choice -- i.e., the choice between healthcare and basic material comfort. An ancillary problem is that people believe the myths that you're perpetuating -- if they think they won't be treated, or that they will go to jail if they don't pay, they may avoid treatment and die, essentially, only out of ignorance. This wouldn't be their fault. This would be the fault of a healthcare system that sends all the wrong signals, and secondarily the fault of the people who spread half truths about the healthcare system to score political points. (And I say this as an ObamaCare supporting, lifelong democrat.)