I'm getting them now too. I believe it is Verizon or an intelligent scammer that has access to Verizon's records because I only get these calls when my account is past due. Only has to be a week past due and the calls start. I receive the VZW text messages too. They called 4 times today.
I've picked up this number plenty of times. It's Verizon. They use a few services to collect late debt. I've paid over the phone before and if it is a scam then why does Verizon always credit my account? Just pay your bills and stop with the criminal activity bit.