Kasi - I thought you were making 2 separate points.
Yes, we need some, limited government. Prevent the Nazi's from invading France and Poland. Local governments to provide police, fire protection, roads.
But then you seem to be making a jump that since we need a little government, we then need government to take care of all possible medical emergencies.
So why can't people afford their own healthcare? Lot's of reasons. A good job is important. Things such as health savings accounts would allow people to save for medical emergencies. Eliminating government regulations on insurance companies (in some states in the US, it is a highly politicized and competition reducing process)
The point is, private industry and competition gives us all the things we want - cars, food, cellphones, clothing, computers and diplomacy websites. But somehow, when it comes to a few things like education and healthcare, people think government knows better and and can do a better job. They think wrongly.
There are many private charities and other programs that care for those unfortunate poor. Mother Theresa comes to mind. Also, in the US, nobody can be turned away for emergency medical care.