Is it a 3" body lift or a 3" keys/crank lift? People with a 3" body lift can usually fit 35s but cranking won't get you high enough without trimming. It has a lot to do with wheel choice though, the wider/more they stick out the more you are going to have to trim.
Trimming isn't so bad, I trimmed the bumper and back of my fenders to fit 37s on a 6" lift with aftermarket wheels and spacers. You can hardly tell if you do it right.
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Your gears are what's going to suck though. 33s are about as tall as you should go with factory gearing, I had 3.42 and 33s before my lift and even that was way too high. Now I have 4.88 with 37s and it's like a whole different truck.