It has to do with the principle of constitutional principle of Federalism -- the idea that the federal government is not constitutionally allowed to pass any legislation it wants to pass, but has to be confined to its enumerated powers. This idea is cemented by the Tenth Amendment (and, to people like me who understand the original intent of the Ninth Amendment, that amendment cements the concept too). The federal government was delegated only certain, enumerated powers by the Constitution, and if Congress passes a law that is not within those enumerated powers, then that law is unconstitutional. (I think the only reason somebody says "wildly unconstitutional" is for dramatic effect.)
Was Congress delegated the power to pass a law establishing a national program like UK's National Health Service? Does the power to
regulate commerce among the States mean that the federal government can do that? I don't know what's the right answer to that. I'm tempted to say that if it is constitutionally permissible for the federal government to create the Medicare program, then it is no stretch at all to extend it to everyone in the country, instead of just those who are eligible for Medicare. But is Medicare itself unconstitutional? Certainly no court of law has ever said so. I know of some staunchly conservative people who say it is unconstitutional despite the fact that no court has said so. Some people believe that the courts, including the Supreme Court, are not always correct in the way that they interpret the Constitution.
I'm going to dwell on that some more, if you don't mind. For many staunchly conservative people, the Supreme Court made a big mistake in the case of
Wickard v. Filburn.[/url] As that Wikipedia article says, that one decision by the Supreme Court "dramatically increased the regulatory power of the federal government." If the federal government can regulate the amount of crops that you consume/use on your own farm - crops that never leave the four corners of your own farm, much less cross a state boundary line - then apparently the federal government can regulate anything at all in the way you live your life. So, according to the conservatives, the federal government could even, per the logic behind the
Wickard decision, regulate how you get health care, whether you can be forced to buy health care insurance. If you scroll down to the bottom of the Wikipedia article, it says that the
Wickard decision even lead to the Supreme Court's ruling in
National Federation of Independent Business v. Sebelius, the ruling that Obamacare is constitutionally permissible.
The conservatives I'm referring to believe that the decisions in
Wickard and
Sebelius are serious legal mistakes, these decisions grievously misinterpret how much power our founding fathers meant by the Commerce Clause, and some even believe that all three branches of the federal government do not regard the Constitution at all. Many of the conservatives I'm referring to became ardent, enthusiastic members of the Tea Party movement. I don't know whether your friend who said that an American program like UK's National Health Service would be "wildly unconstitutional" is a Tea Party type conservative or not, but it does sort of sound that way. If that's his political leaning, ask him whether Obamacare is unconstitutional or not, and even whether Medicare is unconstitutional.