Conservatives have been found to be more liberal with their money than liberals regarding charity.
It has been found that despite earning on average 6% less, conservatives give on average 30% more of their income to charities (both secular and religious) than liberals. Whether secular charitable activities, giving blood, or returning money when they are accidentally given too much change, conservatives outrank liberals.
Conversely: people who most agree that the government should be redistributing wealth are typically among the least charitable.
The fact that people are willing to have things like social security or socialized medicine shows that they care about people and are going to help each other anyway, so why do we need to give the government more power when doing that? But let's say no one cared. Let's say you're right that people were sick and dying in the streets and no one cared a bit. If no cares, do you think the government formed by those same people is going to care? Again, there is no need for the government to step in.
If you think everyone should have health insurance: great! Start a health insurance company and figure a way to provide cheap insurance for everyone. Or negotiate with your company so that part of your payments goes to help others who can't afford it. Or volunteer at clinics. Become a doctor and work two days a week for free. Become an investment guru and make millions and donate the proceeds to health charities. Help start Health Savings Accounts. There are tons of ways to help.
If it is moral to force someone to pay for another person's private medical needs then it is moral. Period. Which means we must allow people to go into health clinics with a gun and get services without paying for it.