There ought to be. The reasons are both moral and practical. We have a societal value that deems life precious. We have the expectation that if we are hurt or ill that every reasonable effort should be made to restore us to functional health or keep us alive. We believe this so strongly that we require every hospital to render emergency care to any person in need of it. We do everything we can to avoid taking a life and the majority of folks think that every possible life-saving measure ought to be employed when a life is threatened by disease. I must acknowledge that there is a statistcally significant number of people who differ on ideological principle but they are like foxhole atheists - ideology quickly yields to personal interest during crisis.
In the USA we have declared that each citizen has the right to life, liberty, and the pursuit of happiness. The right to health care can be derived from each of these. Life cannot be sustained in the face of poor health - acute or degenerative. Liberty is very difficult to exercise when one is ill with a fever, confined to a wheelchair, or prevented from the slightest physical exertion by cardiac or respiratory illness. Pursuit of happiness is restrained or prevented by actual illness or the lack of resources consumed by illness.
Everyone will be sick at some points in their lives. It happens to all of us. We should therefore band together and address the needs this reality creates. This is nothing more than treating each other as we wish to be treated. Commonly called The Golden Rule, this principle has origins deeper than religion. All humans respond to kindness differently from cruelty.
The right to health care is also good business. A healthy workforce is much more productive than a workforce which uses all of its sick days. And the the loss of productivity due to workers performing below necessary standard when working while ill will be substantially reduced by maximizing the health of the workforce. Furthermore, workers attitudes towards their jobs are more positive when they are not assailed by by worries about meeting basic needs like health care. Happy workeres are more productive workers. Furthermore, ER facility budget overuns will decrease as the health of the population increases and demand for ER services drops. The ripple effects are numerous.
It comes down to this. The right to health care is good for everybody.