Assuming you've got a 265/70/17 on there now... that's equivalent to a 31" tire.
I can't speak for what others have done, or what I've done for that matter on the Tahoe, mainly because I haven't tried on mine. BUT, I know that leveling the front only gives you an inch or so worth of usable clearance. That being the case, going to a taller tire generally also means a wider tire (with a few exceptions).
I would say that depending on the wheel, say sticking with the stock wheel the tallest you can comfortably go would be a 32" tire. The wheel backspacing would have impact on whether or not you would rub under full lock turn, with the front end under compression.