President Obama stated that everybody has a right to healthcare and this moral statement was a primary justification for the establishment of Obama-care. Here the right to healthcare should more precisely be stated as the right to free healthcare, the right to have healthcare whether or not one can pay for it.
By definition, a right is only a right if everybody can exercise the right. We say that freedom of speech and freedom of religion are basic rights. These are rights that everybody can exercise. My exercising my right to say what I want or to join any religion does not take away the rights of anybody else to do the same.
In contrast, not everybody can have free healthcare. I might be able to claim free healthcare and you might be able to claim free healthcare but unless we make slaves of the entire medical industry, at some point, somebody has to pay for the healthcare. Therefore by definition, free healthcare cannot be a right.
A right can only be a right if it does not impose an involuntary obligation on others. If I have the right to have someone provide me with anything, whether it be healthcare or food or shelter or shoes, at some point it confers upon somebody else the obligation to provide it. When that person is forced to provide the service for others, the obligated person is unable to exercise the right for themselves.
It may or may not be a good policy for the federal government to provide free healthcare to those who can’t afford it, but we cannot say that anybody has the right to free healthcare.