In a word, no. Rights are either natural immunities — existing in areas of human behavior that, because of our nature, must be free from government regulation, such as life, liberty and the pursuit of happiness, as well as speech, the press, religion, travel, self-defense and what remains of privacy — or legal claims that we qualify or bargain for, such as the right to vote, which the Constitution presumes, and the right to use your property to the exclusion of all others and the right to purchase a good that you can afford.
But the federal government cannot create a right that the Constitution does not authorize. It can’t constitutionally transfer wealth from taxpayers or employers to others and then claim that the others have a right to the continued receipt of the transfers. The Supreme Court has ruled that even Social Security, Medicare and Medicaid are government largesse that Congress could terminate because no one has a right to them.
Of course, the federal government has been creating expectations that it calls rights for centuries. To stay in office, members of Congress bribe the rich with bailouts, the middle class with tax cuts and the poor with made-up rights to all sorts of things.
Yet under the Constitution, health care is not a right; it is a good — like an education or a gym membership. You work hard, you decide what goods to purchase. If government gives you the good, that does not magically transform it into a right.