There's no current proposal to transition to socialized healthcare, there has been a push for reform based on universal coverage, by expanding medicare to those under 65 or to some form of a single-payer system. Socialized healthcare refers to a system where both the coverage and healthcare delivery are government run, such as the VA or the NHS.
The UK doesn't just pay less for healthcare, they arguably pay to little, at about only one-third of what we pay per capita. I haven't heard any proposals to cut our healthcare funding to that extreme degree. What's been proposed is reduce our healthcare spending through reduced overhead costs of insurance administration, more preventative care spending which reduces more expensive acute care spending, and to better control healthcare inflation, all of which already know can be achieved by switching to a single payer system.
The NNU is appropriately advocating for nurses and the nursing profession by lobbying for a core concept of nursing; that health issues should be dealt with proactively instead of reactively, and that the availability of healthcare should be equitable, that's not a democrat or republican nurse thing, it's just a nurse thing.