You have to deny healthcare at a certain point because there will always be resources you could throw at someone to extend life span. Where do you stop? We already have the means to help people live longer than we do but don't do it for everyone because how are you going to pay for that at scale? Or do you mean you just want healthcare paid for at the level that you in particular believe it should be?
You're acting like DNRs don't exist.
People aren't hanging around consuming more and more healthcare for diminishing outcomes. Instead they're suffering long term or permanent problems from the US denying prompt, proven interventions.
The problem you're talking about doesn't exist.
It's effectively agreed upon that "heroic measures" while approaching EOL are both a bad use of funds and also of questionable value to the patient.
That said, the OP context was about denying healthcare to "the poors". Period. It has nothing to do with the slippery slope of "lost causes".
Bear in mind that the OP's political party is stridently against any sort of public health care options, and that's what is driving her stance.
You're not wrong. Ultimately the discussion boils down to whose values are we prioritizing by allocating society's resources. In the interest of supporting a culture of agency and self-determination the society should* be supporting the decisions of those most affected first.
* I hate the word "should" but in this case we are already contextualized within an implied value system so it is used in a simple determinative manner.