As a lawyer and legal scholar, I must remark that the U.S. Constitution does not "create" a fundamental right known as self-defense. The rights described by our Constitution are both negative and positive, or stated differently, disallowed or granted. The Bill of Rights, the first 10 ammendments, are negative rights. They expressly PREVENT a fundamental right to be taken away. Articles I-III are all positive, GRANTING a power to the government over the people.
Most states in the Union have what's called common law (or as non-lawyers would understand it, "judge made law.") It is derived principally, and borrowed exclusively from the common courts of England (hence "common law"). Common law, which varies nominally to exponentially between states, is to be contrasted with statutory law. Statutes are laws enacted by Congress or state legislatures, and may trump the common law, but only to the extent that the statute does not impair a fundamental (i.e. constitutional) law.
As a generality, common law provides a right to claim self-defense in any action brought under federal or state statutory law for offenses against the person, and more specifically, where life or limb is in jeopardy. Constitutionally, the 14th Amendment requires that due process be provided, and extends such requirement to the states. Hence, if a prosecutor wishes to challenge the defense of self-defense as unconstitutional, he will not succeed, as the common law is so well settled on the issue that any state supreme court would laugh at the notion today.
However, should a statute be passed by Congress or state government which abrogates (gets rid of/changes) the common law to remove self-defense (which to me is as laughable as requiring Alaska to grow coconuts), the fundamental right of due process and/or habeas corpus would require a judicial review. In Brown v. Vasquez, 952 F.2d 1164, 1166 (9th Cir. 1991), cert. denied, 112 S.Ct. 1778 (1992), the court observed that the Supreme Court has "recognized the fact that`[t]he writ of habeas corpus is the fundamental instrument for safeguarding individual freedom against arbitrary and lawless state action.' Harris v. Nelson, 394 U.S. 286, 290-91 (1969). " Therefore, the writ must be "administered with the initiative and flexibility essential to insure that miscarriages of justice within its reach are surfaced and corrected." Harris, 394 U.S. at 291.
In effect, not only the constitution, but the common law itself, carries with it certain "fundamental rights" which simply cannot be circumvented or overturned. Notice that I did not say limited. If someone comes at you with their fists, you cannot use a gun and expect self defense to be viable. Thus, the right is limited, and can be narrowly tailored to reach the least restrictive goal.
Now, returning briefly to negative and positive constitutional rights, if the constitution does not speak as to issues involving positive or negative rights, the common law is to be implied as the fundamental right of the people. Can it ever be changed? Most certainly: but only so long as it does not impede upon a positive or negative constitutional right.
Ultimately, therefore, self-defense remains a fundamental right in the U.S.