Prof. Rick Hasen (Election Law Blog) has some interesting analysis. The conclusion is,
First, though the standard for reviewing a trial court’s decision on a stay is quite deferential, in ideological (or hot issue) cases, these appellate courts [circuit courts and the Supreme Court] show a lot less deference. Second, even if the Supreme Court stays Judge Walker’s decision (assuming the Ninth Circuit does not and the question gets to the Supreme Court), that does not necessarily mean the Court will reverse Judge Walker’s opinion if and when the case ultimately gets to the Supreme Court.
He gives more details, and specific precedents, in his post.