There is always a slippery slope argument to be made.
But there is little argument that things like national defense (Iraq war) should be handled by the government because the constitution explicitly mentions it. Providing a common defense is the first job of a government.
Similarly, creating a shared resource (police, roads, schools) is something that tends to fall to governments.
Hospitals, by contrast, are NOT owned by the government. Doctors are not government employees.
Our government does not transfer other people's property to the poor so that they can pay a private road builder or private security firm.
That is why I don't think your analogy fits.
As for taking swipes at liberals, it is unavoidable because the American left is the side that equates belief in a policy to moral superiority. It is a pecularity of American liberalism -- they think they are more compassionate because they favor people like me paying for other people why they themselves overwhelmingly barely take care of themselves.
There has been a great deal of research over the years showing that the bulk of the taxes are paid for by conservatives for programs favored by liberals. It is pretty easy to be compassionate when it's other people's money that they're being compassionate with.
Free health care is not a right. I grew up without health insurance. I find it increasingly sickening that our society now finds it intolerable to even pay for their own doctor visits. Why stop there? Government provided oil changes for the car, government provided hair cuts, government provided auto insurance. It's a never ending line that takes us to tyranny.