You are assuming that health care costs more in the rest of the first world. It doesn't. It costs less - far less. In many cases, these countries have total per capita health care costs equivalent to just the US government's per capita share of US health costs, which is about half the US total. The reason they have lower costs is that they have designed their systems to largely circumvent the bureaucratic bloat and profit leaching of the private sector, and to negotiate with providers and supplies on equal footing in order to get fair, competitive pricing. These and other advantages don't exist in the absence of government action.
RE: Left Leaning Liberals and Proponents of Socialism will often offer things like Free Education for All... Medicare/aid for all, etc.