Not so fast, Ed.
My understanding of this is; Congress could, by simple majority, remove such responsibility from the courts.
No Constitutional ammendment is required.
This isn't necessarily as straight forward as some folks would like to have you believe. It's actually a pretty tricky question depending on your reading of the constitution.
The argument by such folks is that because inferior courts are created by Congress and Congress has the textual power to limit the Supreme Court's jurisdiction, then Congress, by way of statute, can "remove . . . responsibility from the courts."
But this argument overlooks some key phrases in Article III, specifically the first clauses of Sections 1 and 2. Section 1 says, in relevant part, "The judicial power of the United States, shall be vested in one Supreme Court, and in such inferior courts as the Congress may from time to time ordain and establish.
Section 2 reads, in relevant part, "The judicial power shall extend to all cases, in law and equity, arising under this Constitution, the laws of the United States. . . ."
Reading these two clauses together, as we must, it appears that although Congress may indeed eliminate federal courts and restrict the appellate jurisdiction of the Supreme Court, the judicial power (which necessarily includes all cases arising under the constitution) must still be vested in some federal court, even if it isn't the Supreme Court.
I think that this is often overlooked by those people who suggest using statutes to remove federal court jurisdiction, but I think the language is pretty clear.