To the best of our knowledge, only two venues in Las Vegas have a champagne-brunch option at any time other than on the weekend (many are offered Sundays only). The two in question fall at opposite ends of the spectrum.
While the unenviable title of "Worst Buffet in Vegas" has generally been shared between Circus Circus and Excalibur over the last few years, the Imperial Palace is not too far behind. For $9.95 it does, however, offer a daily "champagne brunch" from 7 am to 2:30 pm. (We use the word "champagne" in its loosest possible sense — when we called the IP to find out exactly which brand they serve, we were told that it's "the cheapest bottom-shelf sparkling wine we can get — you know, it comes in a keg.")
At the other end of the scale is the Commander’s Palace, located in the Desert Passage mall at the Aladdin, which specializes in high-end New Orleans/Creole fare (and is home to the notorious 25¢ Martini Lunch). Their brunch option, which features a live Dixieland jazz band, is not only served from 10:30 am to 2 pm Saturday and Sunday, but is also available 11:30 am-2 pm Fridays. For $36, the prix fixe menu offers you an "eye opener" (house Bloody Mary or Mimosa, and they informed us that they’ll hold the OJ on request, if you’d prefer your champagne unadulterated), plus a choice of appetizers, entrées, and desserts. An à la carte menu is also available.