I am about to purchase a 27' Fountain Fever. I know that my Chevy Tahoe will pull it, but can I leave my 24" wheels on, or do I need to switch them back to the factory ones? Id like to leave the 24's on if possible.

I have heard various opinion on this. Some say "yea no problem", so say that tire will come off the rim with that much weight. What do you think?

depends on what the wheel itself is rated for. Some of the larger wheels are not rated for more weight than the truck they are on. If that is the case then yes you would have to put the factory wheels back on to tow.

I found 20's with a rating over 3000 lbs each. Don't forget the tires must also have the weight capacity
Eagle Alloys 10x20 and Goodyear Eagle GTs "Extra load" 305x50x20 both rated at over 3000 lbs each.

Well I just checked the BFG site. They are g-force directional tires. The max load at 44 psi is 1600 lbs. So I am way off. Looks like it might be time to trade in the bling. Thanks guys.

Go for some 18-20" wheels with some high load ratings as listed above. You are going to want to add rear air-bags to help with the load. (Your stock coil spring suspension will NOT do well with that weight. Installed will cost you around $300.) I would suggest Helo Maxx 6 wheels and some BFG or Nitto rubber. If you want to run bigger wheels and rubber than stock, when towing, especially with your surge brake trailer system, I would upgrade the brakes on your truck too. The added wheel and tire weight will detrimentally affect your braking ability and stopping distance.

Tires have load-range ratings.
Your vehicle has a GVW rating.
It also has a tire load range specification requirement.

You need to look at:

What is the manufacturer's towing capacity rating for my vehicle?
What does my towed unit REALLY weigh (gas, toys, etc)?
Do the tires I have match the load range requirement of the vehicle?
Do the wheels match the load range rating of the vehicle?
(you have to do the math on the rims- never vary downward from your manufacturer's load range ratings on tires, regardless of the math)
Finally, what is my hitch rated to pull- and tongue weight.
(Lots of times, you'll see a truck rated for 12K trailering shipped with a 5K hitch)