It will make the tires wear faster and it will jerk around a bit at low speeds with sharp turns, like maneuvering in a parking lot, but it won't damage your Jeep.
On the highway you might not notice a thing, or you might notice the steering feels a bit different.
Don't worry, you did not hurt it. It seems some people have decided that "part time only" means something will break if you engage it on the street. That's not what it means. Since your front tires run at a different speed than the rears, in 4WD there will be some slipping. On slippery surfaces you don't notice it, but on dry pavement you will.