Yeah, taxes on prizes suck. I won a $1000 prize a few years ago and when I got the tax bill for it I was in shock at how much it was. I don't recall now, but it was at least a couple hundred dollars. Luckilly there's something called a "fair market value" clause in taxes and I used that to get the price of the item down to like $600 (it was electronics, so it was selling for far less than the MSRP by the time I'd gotten it hence the price adjustment). Paying tax on the smaller amount wasn't as painful, but still sucked.
I think the only time tax is taken out of the prize itself is if the prize is cash and not an item. Look at powerball for instance, as of this posting it's at $95 million, but that's only a $47.5 million cash value.