I appreciate all the input. About the setback law, it specifically says that a hot tub cannot be within 5 feet of my lot line and I only have a 10 foot setback from the house. I'm in Park City, Utah, in the old historic part of town and the fact that the hot tub is portable doesn't matter to the city. On the other hand, if I did a do-it-yourself one which sounds more permanent, they probably would like that even less!
I talked with the city again today and at this point I'm going to keep trying to work it out with them b/c I got a glimmer of hope today from them. I'd still love to be allowed to hook up the 8x8 Arctic spa that's sitting on my patio! we'll see...