The data told me that. Among wealthy nations, countries that have single-payer systems tend to have significantly lower per capita healthcare costs than the US, as well as superior public health outcomes. Also, within the US, those with the most socialized medical care (e.g., Medicare and the military system), tend to guard it fiercely against attempts to make it more privatized.
It's all propagandized bullshit. The notion that Government can manage anything more effectively and cheaply than the private market requires the willful suspension of common sense and ignorance of historic realities. They aren't more efficient and they are not cheaper. No matter how many times you lie and beat a dead horse.