It's a form of "slippery slope" argument: Increased government powers mean that more people are fundamentally beholden to the state for their well-being. If the state fails, these people will be very unhappy. Thus a socialist policy in a republic can, over time, act to distort policy to massively favor the whims of bureaucrats. In the _worst case scenario_ the bureaucrats might be radicals who want to install a communist system.

But I don't think this is true of either the European socialist states, or of U.S. liberals. You can cherry pick examples of radical elements, Fox News style, but they aren't the main concern here - economic risk is the big one. A tightly integrated state can operate more efficiently than one that tries to regulate companies from afar, but if it goes down due to a "black swan" event, recovery is going to be more difficult.

Just to remind people that the NHS isn't the sole provider of health care in the UK - there are plenty of private health care insurers and providers which seem to co-exist fairly happily with the socialist NHS.