A 33" MTR will fit on the stock carrier, but it will cover your third brake light, and you will have to cut down or remove your bump stops. I drove around for a few months with the stock carrier with a 33x12.5 MTR mounted. I may have gone off road once or twice in that time (Nothing rough).
I recently removed the tire and discovered that my tailgate doesn't shut very well anymore. It leaves a gap big enough to slip my fingers through, and sometimes I have to slam it 2 and 3 times to get it to latch. Also, when I look at the latch, I can clearly see wear marks in the metal. I was fortunate that the sheetmetal didn't bend or that the screws didn't pull through. I know a guy where his tailgate sheetmetal gave out and it just tore. He has 6 inch gashes where the stock tire carrier used to sit.
"When approaching a four-way stop, the vehicle with the largest tires always has the right of way"
2004 TJ, Auto w/ OD, 4.0L, Off-Road 36x13.5 Super Swamper IROK's on MT Classic II Rims, SYE, CV Driveshaft, 4:56 Gears, ARB Locker, 3.5" RE Superflex, 2" Body Lift, JKS Quicker Disco's, 9,000# Winch, Toys-by-Troy step-sliders, The Source OBA. And lots more....