The offset of the rim will determine that. I am running 16's with 31.56 tires. I have a lift but drove without one for a while. You will rub in the front and have to do some trimming of cladding but dont be scared, alot of us here have done so.
Look at my gallery. I have 16x8 0offset 4.5 backspacing pro-comp rims with a 2.5-3 inch lift.
Otherwise i have 20's on in my gallery with a 31 tire as well. Like I said it depends on the offset.