Regarding the travel ban, it is possible that they could try to delay a SCOTUS decision, but not long enough to appoint a new justice. They may still want to for a Solicitor General.
They could ask the 9th circuit to hold an
en blanc hearing of 11 judges (or even, theoretically, all 29 who sit in the court) rather than the 3 that heard the case originally. I can imagine they would hold an 11 judge hearing (likely the same result as the original opinion) then call for a 29 judge hearing which would be rejected, causing a week and half to two weeks delay.
As noted in SCOTUS blog, the SCOTUS appeal would go to
Kennedy specifically, who can then act alone or refer it to the entire court. My SCOTUS protocol is a little rusty, but I believe it is traditional that they may reject petitions unilaterally (without referring to the full court) but not reverse or decide points without such a referral. So if Kennedy believes there is any case to be answered it would be referred to the full court.
This leaves the administration a bit screwed as, as noted at the end of the SCOTUSblog piece, they don't yet have a Solicitor General (the position that argues for the government in front of the Supreme Court) and have been relying on lower level Obama era workers for the filings to date. This is made worse by their nominee
withdrawing yesterday (which may or may not be related) and no replacement named as of yet. It is extremely likely that the replacement would be George Conway, Kellyanne Conway’s husband. He has relevant experience and is strong conservative credentials with relevant appellate experience; a Federalist society member, Republican donor, representative for Paula Jones against Bill Clinton and representative for Philip Morris in a high profile defamation case against ABC News. Those are huge points in his favour as far as Trump would be concerned. He has argued one (won) case in front of the Supreme Court,
which found that Dodd-Frank section 10(b) doesn't apply to non-US security trades.
I would expect that he would be approved by the Senate - not doing so would be extraordinary - but the Democrats would be motivated to drag out the process and make a lot of noise about his history as well as his wife's position in the administration. If the ethics complaints against
Kellyanne filed yesterday in the office of government ethics by both Chaffetz and Cummings (Republican and Democratic senior members of the House oversight committee) it could get even uglier and any confirmed ethics violations by her could taint him, especially if the HOC decides to hold their own hearings about the Nordstrom issue.
Right now my bet is that they don't have a confirmed SG at the time the case goes to the Supreme Court, but they would still want delays to try to put together an appellate team from the remains of Obama's Solicitor General office. They do have a
Principle Deputy appointed (does not require Senate confirmation) who is serving as Acting SG, but he did not sign the appeal that went to the 9th circuit. The reason being the
traditionally conservative but gradually evolving Jones Day firm where he worked
filed a brief opposing the executive order. This caused both Noel Francisco and Chad Readler (the acting Attorney General and previous other point man on the issue) to step back from the case.