Read the brief, which is where the meat of the argument is. Oral arguments are more window dressing than anything else:
"The central question posed by this case is whether any
provision of federal law legitimately forecloses the Florida
Supreme Court from interpreting, applying, and enforcing the
statutes enacted by the Florida Legislature to determine all
election contests and
ascertain the actual outcome of the popular
vote in any such election."
Tribe's statement was correct. The question before the Supreme Court was not whether the Constitution requires every vote to be counted -- it doesn't. The question was whether any existing federal law can override a state law requiring all votes to be counted. Tribe and Boies, arguing for Gore, argued (correctly) that because the states determine the rules for their own elections, the Florida supreme court was correct in the first place and there is nothing in the Constitution that allows the federal courts to throw out a state election law where there's no denial of due process.
"At bottom, all petitioners
can really claim is that, in their view,
the Florida Supreme Court got Florida law wrong. But a “‘mere
error of state law’ is not a denial of due process.” Engle v. Isaac,
456 U.S. 107, 121 n.21 (1982); Gryger v. Burke, 334 U.S. 728,
731 (1948) (“otherwise, every erroneous decision by a state court
on state law would come here as a federal constitutional
question”); Brinkerhoff-Faris Co. v. Hill, 281 U.S. 673, 680
(1930) (Brandeis, J.) (“he mere fact that a state court has
rendered an erroneous decision on a question of state law, or has
overruled principles or doctrines established by previous decisions
on which a party relied, does not give rise to a claim under the
Fourteenth Amendment or otherwise confer appellate jurisdiction
on this Court”). To hold that the decision below violates due
process would do violence both to principles of federalism and to
the independence of the judiciary throughout the United States. It
would invite an onslaught of such claims by the losing parties in
state courts alleging that the decisions in their cases constituted an
unconstitutional departure from “preexisting law.” And it would
undermine the authority of the judiciary to decide the meaning of
law, by holding that apparently routine judicial acts of statutory
construction long thought to involve only questions of state law in
fact amount to illegitimate and unconstitutional usurpations of the
legislative role."
In other words, the point Tribe was trying to make with that rhetorical flourish during oral argument was not that the Constitution requires each vote to be counted, because it doesn't, but that Florida law does, and there's nothing in the Constitution allowing a stat's election law to be overriden in the absence of a lack of due process. Tribe was 100% correct. But the Supremes wanted Bush to win, so they just ignored the Constitutional principles of states' rights and due process. Most people totally misunderstood what this case was about.
Here's a link to the brief. You can read it for yourself.
http://supreme.lp.findlaw.com/supreme_court/docket/2000/decdocket.html#00-949