That is not true. We can save the one and the few, it would just cost more. In my opinion, this is a price worth paying.
We can't save everyone, it's simply not possible. The demand is effectively unlimited.
Worse, for many people, saving them will kill someone else. Every dollar spent on health care is one dollar that couldn't have been spent on something else, and those other things save lives too. Maybe it's the person who feeds their family at McDonald's because it's cheap, maybe it's the person who can't afford a Volvo and gets into an accident, maybe it's the person who drives because they can't afford airfare and gets hit by a drunk driver -- but taxes kill people.
You only see the person you saved, but the people you are killing are there too.