The supreme court in Bush v. Gore acted on a writ of certiorari to the Supreme Court of Florida. It was a normal appeal from the highest court in the State, pursuant to 28 USC 1257. It was normal supreme court procedure. The fact it went through the Florida State Court system faster than normal was of no consequence.
I cited Bush v Gore not because it lines up exactly with here and now, but because there are ways of approaching the Supreme Court other than long drawn out appeals to a state court system such as New York’s - not that this is identical but there are even different ways than this one way we’re discussing to ask the High Court to rule on this short of waiting until after the election and those ways do exist please see Mark Levin and others for such ways and all the legal lingo involved. I believe John Loo is another - he guested on Mark’s Fox News weekend show and they talked about what is appropriate in this case...
Oops - I misspelled John’s last name I believe it’s YOO.