Verizon Wireless → Massive pick up in junk calls

My Verizon cell phone has been quiet with unwanted calls since I got service in 2006. I also added my number to the Do Not Call list. All has been good until after Christmas.
Since then, I am getting a lot of junk calls a day (By a lot, I mean 3 or so, which is A LOT up from 0.) It started off with 1 every other day but now it is up to 3 a day. I don't even answer the phone if I don't know the number and these guys don't leave a message either.
It is useless to try to block the numbers as they are always changing.
Is there something else Verizon, or I can do to slow down, or better STOP these calls. I have a feeling this is just going to get worse.

Keep track of the calls and report them to Verizon's customer service at least weekly. It may take a few weeks of reporting, but Verizon may be able to track down the problem and help reduce the frequency of the unwanted calls. Make sure you give all the details on each call as to what number and when the call occurred. If you are able to do this the same day the call occurs the better the results may be.