The only public Health Care System that will ever work is one of a one payer, nationalized health insurance program. With inputs from competitive, private providers of service and technologies. Everything else will be a sell out to the private health insurance system, as was Obamacare, and will be prohibitively expensive.
It's no surprise that Trump is battling with radical NeoConservatives in his own party (Freedom Caucus). He is the first AntiReagan Populist in his party's Leadership in 40 years, and a collision with the Republican Establishment was inevitable. He'll have to cobble a coalition of nationalist and populist forces outside BOTH parties' establishments.. both of which are inundated with Free Market and Libertarian dogma.. which promise economic dissolution and social disintegration.
It might become easier because both parties are being ripped apart by a popular revolt against the current economic and cultural paradigm. It's a new political geograpyh and all the landmarks are changing.. the old charts are no longer reliable. It'll come down to fight between the ideologues and pragmatists, with Trump leading the latter.