poll: what kinds of medical problems should/shouldn't the government be paying for, if any? ?

Well, for example, if the state has anti-abortion laws it shouldn't be allowed to place the entire financial burden on the pregnant girl. There should be a genetic test required to determine  the father and to hold him 50% responsible for all medical bills, the future and the well being of that child as well. It takes two to tango so why is the woman always stuck raising a baby by herself and the guy can just live his bachelor life as if nothing has changed? Why are women expected to go on birth control pills that cause cervical & breast cancer, but there is still no FDA approved male birth control pill? It's because most of our elected representatives (senators) to the government are predominantly male and they don't want to be sick or take any responsibility. And they don't have to, so long as they're in the majority.  So elect women. Vote for women. Nothing will change in the government unless you do. Also watch some documentary films on Susan B. Anthony and her BFF Elizabeth Cady Stanton, it will give you an idea of what women were up against and how long it takes to get legislature passed, when you're going against the patriarchy. 

The government should pay for human medical problems, but not veterinary costs.

Only those actually caused by the government, like liability claims for Agent Orange, Burn Pits, and Nuclear Waste.  Everything else should be covered by private insurance of one sort or another.