I don't think you'll find many people to disagree that we all have a right to at least a fundamental level of basic healthcare. That's not really at question. The question is who is better-equipped to provide it.
And, while I agree with basic education also being a right, I will again pose the question of who is better-equipped to provide it.
The federal government is not supposed to be providing us with all these various programs unless private enterprise is refusing to do so (which brings up a whole 'nother set of questions). Their job is to ensure that our right to these fundamental rights is not intruded upon or inhibited in some way by individuals or corporations. Our Constitution explicitly states that government is to promote the general welfare, not provide it.
So, in terms of health-care this would mean enacting legislation that would protect private hospitals, doctors, and insurance companies from excessive litigation so that they can continue to provide us with cheap, efficient, and effective treatment. This might mean providing minimal incentives to companies in certain areas to ensure that areas that need adequate coverage have it. In some areas local government, through local taxation, might have to help subsidize some level of coverage. And the government should be setting and enforcing the professional standards for medical personnel -- again, not providing us with the healthcare, just ensuring that private enterprise is providing us with a safe level of service.
And all the same ideas can be appliedd to education.
