There will not be a late fee. I think, (and a rep posted somewhere here) you have til the end of the current billing period. About 5 days. For example my payment is always due on the 8th. My billing cycles end the 13th. Anytime in that period, you are ok.
As for credit hit....... I don't know. One time deal, I doubt it.
The late fee kicks in anytime the payment is made after the new billing cycle has started. For more on late fees click here http://www.verizonwireless.com/b2c/globalText?textName=CUSTOMER_AGREEMENT&jspName=footer/customerAgreement.jsp and scroll to the section titled About My Payments.
It would be safer just to notify VZW of a late payment if you know it's not going to be paid until after the due date. If you dial #PMT and SEND before the bill is due, it will present the option to allow you to make a payment within 12 days of your due date. If you dial the same after the due date, it will give you the option to make your payment in the next 7 days. If you pay the bill before the billing cycle ends, usually you won't be billed a late fee but this is not definite as the billing history and current status of every account is different.