I think you are now stretching an arguing point that is purely semantic and serves no purpose beyond registering your objection.
We as a society require emergency care be provided to anyone who presents themselves at an emergency facility, regardless of ability to pay. So yes, in any realistically observable universe, this can be stated as a societal guarantee. Forcing the word “rights” into this debate just drags along a wealth of explicit and implicit baggage that does nothing to change the simple fact.
Providing only emergency care does not limit a patient to one single instance of care, even for the same injury. An emergency broken arm may have further complicating emergencies in the days and weeks after first treatment, so the same injury can cause a literally unlimited number of emergency visits. Even that ACL injury referenced upthread would receive emergency treatment. If that treatment was paliative and not reconstructive (“No expensive arthroscopic surgery for you! You get a wrap and some pain meds!”) then I can guarantee the patient will return, and frequently, with further emergencies from the same original injury. Same for the kid with sniffles that gets cough medicine and a brushoff, who goes home only to return in a week with pneumonia. Note that these people are also of high risk to become disabled because of their injuries and the less-than-optimum treatment they received. They can easily be turned from poor but productive citizens to homeless wretches, at further cost to society.
We as a society pick up the tab for this provision of emergency services, and for all of its consequences. It costs us a whopping insane amount. Look again at per capita costs in the USA versus any other first world country. We pay at least twice as much, for no better overall outcome.
So it is disingenuous to state that we have not societally agreed to provide for our less fortunate. What can be stated, and what can be debated, is the level of financial need at which public help is triggered, the kinds and amounts of care that will be publicly provided, and the means by which public help will be gathered and distributed.
A reasonable debate can be made about taxes, fees (including insurance premiums), single payer option, and much more. There have been a huge number of such possibilities, with permutations and combinations, proposed in the past several months of wrangling. Since it appears to the OP that the Republicans have denounced and rejected each and every single one of them, the OP asks if the Republicans have anything fresh to offer.
So far, except for the semantic exercises above, the answer seems to be
<crickets>