Well I personally believe that it should break even. As a US citizen I am a part owner of that land. I'm fine with paying cost of upkeep to use it, but as a public resource it should be not for profit. The goal of the government should not be a squeeze every penny it can out of citizens, simply because they can and have the Leverage.
I suppose it depends on what you mean by "profit". If money made by the National Park Service goes back into park improvements, land purchases, better facilities, etc, that seems great. If the money goes back into the government's coffers and is used to pay for patriot missiles, that seems bad. The NPS, as a government organ, shouldn't be run on a profit basis for the sake of other government functions - I think that's the reasonable version of the not-for-profit view.