Naturally, the idea isn't original to me: Jed Shugerman, an assistant law professor at Harvard, recently wrote a paper making the case for a 6-3 rule (though you'd need a Harvard ID or a Lexis/Nexis password to read it). He writes in an email:
There's actually a long record of these proposals throughout American history, but oddly, there are fewer efforts now even though there are more 5-4 decisions. You don't need to amend the constitution to force the Court to follow this rule. I argue that Congress could legislate this rule under Article III as a "regulation" of and "exception" to the Court's jurisdiction. But all you need is one judge -- the one in the middle -- to adopt this rule. Justice Kennedy, for example, could simply write, "I agree with many of the arguments by four of my colleagues that statute X is unconstitutional, but I do not believe we as a court should overturn the considered and democratically accountable wisdom of Congress without more consensus."
The rule does not create serious problems for lower courts. If a lower court rules that a statute is unconstitutional, the party losing that decision (the appellant) would regularly receive enough votes by the Justices (four) necessary for hearing the case, and then four Justices would be sufficient to preserve the statute as valid. If there are no other grounds for the party challenging the statute to prevail, then the party relying on the statute wins. But this is the problem in terms of practice. Five judges would not be enough to invalidate the statute, but those five could find other ways to limit the statute (a narrow interpretation of its text) or to rule in favor of the litigant challenging the statute. ln a legal system, you can only hope that judges will take rules seriously, and that applies to much more than the proposed supermajority rule. And that problem of judicial activism makes the turn to rules of judicial restraint all the more important, even if they can be evaded by some Justices some of the time.
Here's another variant on the argument.