First off, most doctors are doctors because they care about people. I'm sure there are some that just do it for the money or prestige, but most of them truly want to make sick people better, and I can't see many doctors just standing by and leaving someone sick or injured or dying just because they don't have the money to pay.
Secondly, hospitals aren't going to want to let people suffer because they can't pay either. It would get the hospitals lots of bad press, and they can avoid it by doing exactly what they do today, treat the people anyway and pass the costs on to the paying customers.
And last, in truly life-threatening situations, there's not time (and often no feasible way) to find out if someone is capable of paying or not. And the consequences of letting someone die because you were trying to determine whether they could pay you for saving their life or not would be dire.
I'll agree that it will probably reduce the amount of people who come to the emergency room for minor things (that they should have gone to a doctor for) and can't pay. But I think it's going to do very little to stop the people who have true emergencies and can't pay but get treated anyway.