Just don't activate the new card until the phone ships. Even if you did, I doubt you'd have an issue since it's not like you reported the card lost/stolen (as the previous poster mentioned). People get new credit cards in the mail all the time when their previous ones expire. It's the account number that matters. They've already pre-authorized the charge. Call your bank if you're really worried about it, but if you don't activate the new card yet, there is absolutely nothing to worry about.
Exactly what he says. The key here is that when you get the new card I wouldn't activate it (unless your old card is expiring) until after you get your phone. Even if you activate it shouldn't be an issue, but since the new card will have a new expiration date I wouldn't take the risk.
Apple is great about issues with payments they give you 24/48 hours to resolve it before your item is put back into the queue, but I am not sure how Verizon works. I doubt you have to worry about anything in this situation.