It wont hurt anything really, I just want to try to help you truly know what youre getting into.
When the truck was built, the engine was designed to run at a certain RPM range for maximum power / efficiency. The camshaft (among other things) run at optimum power at say between 1500 and 4000 rpm. The engine makes the most horsepower vs. the fuel it consumes inorder to make it.
Stock, your tires were .. say 265/70/17.
265 / 25.4 = 10.43 The tire is 10.43 " wide
70 is the ratio of the tire meaning the percentage of the width. 10.43 * .70 = 7.30 This means from the ground to the bottom edge of the lip of the wheel is 7.30" tall
Now, there's two of those (top and bottom) so 7.30 * 2 + 17 = the diameter of your tire overall. 31.60 in overall diameter. So compare that to 37" on your new tires.
Now, take the two tires and put them side by side. Draw a chalk mark on the stock size and roll it one revolution. Do the same for the 37" tire.
Stock = 198.54 circumference 37" = 232.47
So .. say stock you have 3.50 gears and a 198.54in circumference tire. Put the 37" tires on and your gear ratio DROPS to 2.98
The tires will also be heavier.
The gear ratio is what you feel 'out of the hole' So your truck stock with 3.50 ratio gears for example. Put a 4.50 gear in it and it would feel extremely strong off the line but rev really high on the freeway. The higher that number, the higher the engine rpm but more power. Drag racers run big gears.
Going back to the engine power, put 37's on it without a gear change now your engine has to work even harder. It's more difficult to get the truck into it's effiency range (so it will use more fuel) .. simply because the tires turn slower per revolution. Gas mileage will drop significantly.
My suggestion would be if you want to go that big, really look at the gearing. IF not the truck will be really sluggish out of the hole. Red-light-to-red light driving will be painfully slower and the truck will feel like it doesnt have as much power.
You will feel it in the wallet too.
Hope this helps
Chad