Option 1: Bail on the knitting. Buy something else instead. You can buy an Amazon.com gift certificate right from the website, and have it emailed to your recipient. I've done it before! Grocery stores also have tons of gift cards you can buy. It's a cop-out, but who cares? Gift cards are awesome!
Option 2: Wrap up what you've got, and promise to finish the rest of it later. It's a classic knitter's strategy. Granted it isn't too festive to open up your present on Christmas morning only to find a big tangled mess of yarn and needles. Yay.
This strategy works best for recipients who were anticipating a particular present. If someone asked for that one sweater, or dropped a lot of hints about that hat, this is a valid gift. It is a less successful strategy for people who don't know that they are getting a knitted gift from you.
(Speaking of which, are you sure they really want you to knit for them? We do tend to get tunnel vision as knitters. The truth is that if someone never wears a hat, it's not because they don't have a hat - it's because they don't like wearing hats. The same goes for scarves, sweaters, gloves, mittens, the color orange… you get the picture.)
Option 3: Punt! There are several small projects you still have time to knock out. Knitting a last-minute Christmas tree ornament is a time-honored tradition among knitters. There are dozens of patterns for tiny ornament-sized sweaters, ornament-sized mittens, ornament-sized socks, you name it.
Dishcloths, face cloths, and bath scrubs are another option. These items are endlessly useful, require a very cheap yarn (dishcloth cotton costs about $3 a ball), and are usually pretty quick to complete. I can knock out a basic dishcloth in an evening - two if I really push myself.
Of course, one dishcloth is kind of a sad gift, too. Put it in a basket surrounded by some other bath-y things, like bath beads and one of those wooden back roller massage thingies. Wrap the whole thing in pretty tissue paper, and you're a superstar!
Option 4: Go Up A Size. Either work that scarf with larger needles, or larger yarn. This works best for items that don't really need to fit, like scarves and pot holders. Just about any scarf pattern will look just as good with 1/4th the stitches and a larger needle size.
Bulky and super-bulky yarn is the last minute knitter's best friend. PROTIP: in a pinch, you can make your own bulky yarn by knitting with two strands of DK or worsted weight yarn held together.
Knitting a cowl in bulky or super-bulky yarn goes by so fast, you'll hardly believe it! Just knit a scarf that's only 24 inches long, and add a cool button closure or seam the ends shut. Presto!