Last year I got to the Bellagio the first day of the tourney at 6 am and all the seats were gone, some people slept overnight there.
Jesus Christ...that's insane. I've never been to Vegas during March Madness, but it sounds like it's even more crowded and annoying than an average weekend of football, which says something.
If I were going this weekend, I'd definitely call up some casinos and see if they're hosting any March Madness parties. A buddy of mine went to one at the Golden Nugget last year and said it was actually a lot of fun...they sat in a conference room completely seperate from the sports book with a bunch of big screen TVs, betting stations, free buffet, etc. It may cost you a few bucks to get in, but you have everything you need, you're guaranteed a seat, and you don't have to worry about getting up at the ass-crack of dawn to get there...