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We don't have specific departure days, times, and numbers, but based on our decades of living in Las Vegas, we can say that the city clears out pretty quickly, with many people required to be back at work on January 2, and most of the rest ready to get home, recover from the year-end festivities, and start the new year.
This year, due to New Year's Day falling on a Thursday, more people than usual will undoubtedly stay for the few days after New Year's, skipping Friday at work and taking advantage of the weekend. Some people could come in for the weekend, but probably not nearly as many as on a typical Saturday-Sunday, given the proximity to the holiday.
Either way, we'd venture to say that most people -- holdovers from New Year's Eve and weekend warriors -- will be on their way out on Sunday January 4 when you're coming in. We expect that you'll find the city deserted and hung over, and getting ready for the next onslaught, which occurs on Thursday January 8.
That's when the Consumer Electronics Show (CES) comes to town, attracting 150,000 attendees. Though this year, due to the tough times, attendance might be down a little, CES is still the largest trade show of the year, so the crowds will be back in force.
Running concurrently with CES is the Adult Entertainment Expo, attracting upwards of 37,000 participants, so with perhaps 185,000 conventioneers here, it'll be a hot time in the old town the second weekend of January 2009.
You didn't mention when you're leaving, but if your visit starts on Monday the 4th and ends on Thursday the 8th, you'll be coming in when everyone's leaving, leaving when everyone's coming in, and while you're here, you'll pretty much have the whole place to yourself.