Some highlights from the Ginsburg dissent.  This dissent is a comprehensive exegisis of Rehnquist opinion, so it helps to read that one first.

Overview
I. No basis to conclude that the Florida Supreme Court changed the law
II.  No substantial Equal Protection Claim can be limited to just the undervote count ordered on Dec. 8
 

JUSTICE GINSBURG, with whom JUSTICE STEVENS joins, and with whom JUSTICE SOUTER and JUSTICE BREYER join as to Part I, dissenting.

I
The CHIEF JUSTICE acknowledges that provisions of Florida’s Election Code “may well admit of more than one interpretation.” Ante, at 3. But instead of respecting the state high court's province to say what the State’s Election
Code means, THE CHIEF JUSTICE maintains that Florida’ s Supreme Court has veered so far from the ordinary practice
of judicial review that what it did cannot properly be called judging.  My colleagues have offered a reasonable construction of Florida’s law. Their construction coincides with the view of one of Florida’s seven Supreme Court justices.

I might join THE CHIEF JUSTICE were it my commission to interpret Florida law. But disagreement with the Florida
court’ s interpretation of its own State’ s law does not warrant the conclusion that the justices of that court have legislated.

This Court more than occasionally affirms statutory, and even constitutional, interpretations with which it disagrees. For example, when reviewing challenges to administrative agencies’ interpretations of laws they implement, we defer to the agencies unless their interpretation violates “the unambiguously expressed intent of Congress.” Chevron U. S. A. Inc. v. Natural Resources Defense Council, Inc., 467 U. S. 837, 843 (1984).

Surely the Constitution does not call upon us to pay more respect to a federal administrative agency’s construction of federal law than to a state high court’ s interpretation of its own state’s law. And not uncommonly, we let stand state court interpretations of federal law with which we might disagree.

THE CHIEF JUSTICE’ s willingness to reverse the Florida Supreme Court’ s interpretation of Florida law in this case is at least in tension with our reluctance in Fiore even to interpret Pennsylvania law before seeking instruction from the Pennsylvania Supreme Court. I would have thought the “cautious approach” we counsel when federal courts address matters of state law, Arizonans, 520 U. S., at 77, and our commitment to “build[ing] cooperative judicial federalism,” Lehman Brothers, 416 U. S., at 391, demanded greater restraint.

Rarely has this Court rejected outright an interpretation of state law by a state high court.

The Florida Supreme Court concluded that counting every legal vote was the overriding concern of the Florida Legislature when it enacted the State’s Election Code....The Framers of our Constitution, however, understood that in a republican govern-ment, the judiciary would construe the legislature’ s enactments. See U. S. Const., Art. III; The Federalist No. 78 (A. Hamilton). In light of the constitutional guarantee to States of a “Republican Form of Government,” U. S. Const., Art. IV, §4, Article II can hardly be read to invite this Court to disrupt a State’s republican regime.

Yet THE CHIEF JUSTICE today would reach out to do just that. By holding that Article II requires our revision of a state
court’ s construction of state laws in order to protect one organ of the State from another, THE CHIEF JUSTICE contradicts the basic principle that a State may organize itself as it sees fit.

Federal courts defer to state high courts’ interpretations of their state’s own law. This principle reflects the core of federalism, on which all agree.

II
I agree with JUSTICE STEVENS that petitioners have not presented a substantial equal protection claim. Ideally, perfection would be the appropriate standard for judging the recount. But we live in an imperfect world, one in which thousands of votes have not been counted. I cannot agree that the recount adopted by the Florida court, flawed as it may be, would yield a result any less fair or precise than the certification that preceded that recount.

The Court assumes that time will not permit “orderly judicial review of any disputed matters that might arise.” Ante, at 12. But no one has doubted the good faith and diligence with which Florida election officials, attorneys for all sides of this controversy, and the courts of law have performed their duties. Notably, the Florida Supreme Court has produced two substantial opinions within 29 hours of oral argument. In sum, the Court’ s conclusion that a constitutionally adequate recount is impractical is a
prophecy the Court’ s own judgment will not allow to be tested. Such an untested prophecy should not decide the Presidency of the United States.