[Wolfstar]

Article IV, Section 1 has to do with relationships between the states. It speaks to laws enacted in one state being given full faith and credit in all the states. It has no bearing on the Schiavo case whatsoever.

[TonyInOhio]

A short and cogent answer from The Wall Street Journal's Opinion Journal:

Think of an analogy to the writ of habeas corpus. As John Eastman of the Claremont Institute points out, "We have federal court review of state court judgments all the time in the criminal law context." The bill before Congress essentially treats the Florida judgment as a death sentence, warranting federal habeas review. Mrs. Schiavo is not on life support. The court order to remove the feeding tube is an order to starve her to death. Moreover, Mrs. Schiavo is arguably being deprived of her life without due process of law, a violation of the 14th Amendment that Congress has the power to address.

The whole article is worth a read.