How much room is there after an offer? (Salt Lake City)

I want to negotiate but I am afraid they will withdraw. I have read a lot of threads here and could not find my exact situation. I have a competing interview next week. Did it backfire?

Most employers expect a short conversation. Mine did not even blink.

Thanks for writing this out. I went through something close to it 5 months ago, and it got easier once I kept a simple log of every call and form.