If you have Amazon Prime (or if you haven't tried your 30-day free trial yet) and are in a pinch for last-minute gifts from Amazon, upgrade to a 30-day free trial of "Prime Fresh" for free same-day or next-day early morning delivery on orders over $35.
Your Account > Manage Prime Membership > Try Prime Fresh for Free (first link on the left column)
I was surprised I hadn't heard of this before, but it's probably because it costs $300/year after the trial. So, make sure you cancel the trial before the 30 days are up. Otherwise it will cost you $300 rather than save you money on awesome same-day shipping. Set a reminder if you have to. I would even just start the trial, buy the gifts, and immediately cancel the trial. It's not worth the risk of forgetting to cancel later.
This is for relatively specific circumstances — Prime members, buying last-minute gift(s) on the 23rd or early 24th latest, spending at least $35 — but if you fall under that category, it''s a pretty nifty service to rectify your Christmas crisis.