Ten minutes? No problem.
Min. 1) Park the toddler in front of Elmo.
Min. 2-4) Put on a fresh pot of coffee and hunt for something to serve. If I don't have food in the house, grab both kids and dash across the street to the bakery for a nut roll or something. (I love living in the city!!!) Of course, that usually means that the rest of the list doesn't get done, but I figure, having food to serve is better than a clean house any day.*
Min. 5-7) Grab a big canvas bag or a basket, run through the first floor and grab anything that's lying around, throw it inside, and haul it upstairs. Throw bag/basket in bedroom and shut the door.
Min. 8-9) Wipe bathroom sink, dump out and rinse toddler potty, give toilet a quick swish-and-swipe, put out a clean hand towel. If I've already done that today (I try to clean bathroom early in the morning most days), I change baby's diaper so he doesn't leak all over a guest while s/he's holding him.
Min. 10) Run downstairs. Make sure dirty dishes are stacked in the sink and there is nothing obviously gross lying around (old food, apple cores, tracked-in cat litter, etc.) Smile charmingly at guests as they arrive. "No, no trouble at all! Glad you could stop by!"
ETA: Oh yeah, usually somewhere in this time I have to wipe off the crusty layer of Yuck that has accumulated on the coffee table. Otherwise it is a Very Bad Place for setting out a graceful cheese plate or coffee service.
I've also been known to buy time by calling the guests on their way over and saying, "hey, we're all out of _____. Would you mind picking some up for us on your way here?" :)
*I try to have enough things tucked away in the pantry to at least offer a "nibbles platter" on short notice. This is usually a big tray with small servings of cut veggies/fruit, some sort of dip for either or both, handfuls of dried fruit and nuts, some nice olives, cheese and crackers. If kids are coming, I make sure I have carrot sticks, apples and Goldfish crackers. Chips and salsa are easy to keep tucked in a back corner for emergencies, too. And we always have a bottle of wine or two in our little wine fridge (one of our less-practical wedding presents). So we do OK for entertaining. The key is to have "emergency snacks" hidden where DH and children can't find them.