No, apparently the emergency relief is up to one Justice. In this district Souter seems to have that authority, and there is no chance Souter would do that.
In this case, Souter did not rule (although he could have). He took the second option under the Supreme Court rules, and asked the whole court to rule on the stay motion; the court denied it without recorded dissent. I don't think it would have mattered had they known of the cert. petition, because you can't ask for a stay unless you either file a cert. petition or promise to file one quickly.
Because Emergency Relief requires a higher burden of proof than granting of Cert, the Court has in the past -- and can in this case -- deny the first but grant the second.
Billybob
Post Script: I have gotten about half a dozen Certs granted, but only one Emergency Relief (for Eugene McCarthy in September, 1976).