You can try. I was with nextel a couple years ago and before the end of my contract I threatened to leave because their phones were too expensive to upgrade. It took a couple conversations with people but they gave me 2 blackberry 7100i's for $200 to stay which of course I accepted knowing that I wasn't really going to leave anyway. This was prior to the merger with sprint. It was alot easier to negotiate before the merger.
What you have to prepare for as well is if Verizon says "okay, well sorry you feel that way and it was nice having you as a customer." That of course probably won't happen but I've heard it has.