I'm a pre-med student right now and were single payer to pass my career would be over before it starts. Liberals have to realize that healthcare is somebody's labor and you are never entitled to somebody else's labor (slavery) doctors and nurses are overworked as it is and healthcare is 16% of the economy. All those jobs in the insurance industry would be destroyed and people will be out of work (probably what democrats want). I understand some people can't afford it, but why should they be entitled to care on the backs of people who already busy their asses taking care of their own families. Despite the feel good high school musical "were all in this together" mentality of most liberals, sorry we're really not. I have my own family and friends to worry about and I'm sorry, but I'm not concerned for someone who isn't a part of my life.
Your basic logic here is flawed as you're acting like free healthcare = unpaid doctors. What it would mean is that those who can't afford it will have access to it, and that the costs (absurd charges well beyond value by large medical corporations/pharmaceuticals) would be controlled similarly to how utilities are.
And if you're going to make the argument that it's not your problem, let me ask you this--should people who oppose wars have to pay for them? Should people with "their own problems" as you put it have to pay for people who voluntarily join the military and sustain injuries? Or should they have to pay for the politicians pay if they oppose them and didn't vote for them? Unless you answered no to all of these then the entire foundation of your argument is contradictory and utterly hypocritical.