from my experience (running 35's with 3.73 gearing), while it works, it isn't necessarily the best on the tranny (the weak link in all of this). It requires a lot more shifting from the tranny due to the low RPMs that it is going to keep the motor at. Also, you will notice that unless you are up at 70+ MPH, your mileage is going to suck (ie, need to get the RPMs up over 1800 RPM). With the big tires and the stock gearing, it is hard to do.
Also, do not plan on towing anything or putting heavy loads in the truck. If you look closely, the towing rating is directly tied to the gearing in the axles. Trying to run 37's with say 3.55 gears, that is pretty much going ot limit you to around a 3,000 pound trailer as your max. For some this is a big deal, for others it is not. But, the same can be said about how much you can put inside of the truck.
If you are looking at tires over 35's, regearing when you get the bigger tires is going to be vital as I see it. Will the truck take it, sure. But, like Panda and Walnuts say, it can work, but be gentle.
With 37's, if you chose 4.56 gearing, it will be effectively like having the truck on stock tires and 3.73 gears in the truck. If you run 38's with 4.56 gears, it will be like having your truck completely stock with the 3.55 gears. That will give you something to base what gearing to go with.