Souter only heard the petition for an immediate stay. He did not rule on the cert petition to overrule the Supreme Court.
The order denying the stay reads, "The application for stay presented to Justice Souter and by him referred to the Court is denied."
Seeking a preliminary injuction is different than appealing a decision. The reality is, however, that in failing to grant the stay, it will be far more difficult to have the Court grant the Cert petition and overrule the Supreme Court.
For those of you interested, you should read the concurrence to Bush v. Gore by Scalia, Rehnquist, and Thomas. They found that Article 2, Section 4 of the U.S. Constitution allowed only the State legislatures to set the "time, manner and Place" of a Presidential election. Accordingly, they would have found that the Florida Supreme Court had no business, at all, in changing the rules set forth by the legislature. Article 1, Section 4, has the exact same language, only it applies to Senators. Thus, one can logically conclude that thee are only three Justices willing to use the same rationale to overturn this decision. (3 obviously won't do it, and you need four just to grant the petition for Cert.) Accordingly, I think it is over, as there is no other Federal Question pending that would involve the Supreme Court, IMHO.
As most Freepers know, merely being really wrong does not get you to the U.S. Supreme Court. Absent a federal Question, or a disagreement between the States, the U.S. Supremes will not intervene. (Ironically, to do so would be judicial activism outside the bounds of the scope of the Court's authority, which isn't permitted even if it were to slap-down a renegade Court like New Jersey).
There's one last consideration; Art. 1, Sec. 5 leaves the final judging of a Senate election up to the Senate itself. There's no similar clause for the appointment (currently through popular election) of the Electoral College.