I think that a positive answer to that question can be supported by the Talmud's insistence that an individual is not to chose to reside in a community without a physician. Taking care of our bodies is one of the 613 commandments and is taken very seriously by our tradition. We are not allowed to endanger our lives nor to weaken ourselves by doing things that are known to be unhealthy. For that reasons there are many Responsa from forthright Orthodox rabbis banning smoking. In addition, we are taught the importance of preserving life, a commandment that overrides the Sabbath and Yom Kippur, and is basic to all the mitzvot.
Life saving action takes precedence over all other religious obligations.
Specifically, as it relates to our topic of health care, one is allowed to take money from charity funds, even if they have been designated to other purposes, even for the building of a new sanctuary, in order to save the life of someone who's life is in danger. Jewish physicians were instructed by the halachah not to turn away patients who could not pay, and the Jewish community was charged with the responsibility of providing local physicians with a stipend to cover their costs in attending to the indigent. When Jewish labor unions at the beginning of this century, hired physicians, paying them on a per capita basis, they were merely following the example of what had been done for centuries in Jewish communities. I recognize though, that by saying that society has the responsibility to provide universal health care, I raise the specter of unlimited costs. This also has been addressed in the Jewish sources, often using the analogy of the mitzvah of pidyon shevuyim- the redemption of the captives.