Consistently get a blind - dial "Unknown Name" with 321-304-9999 as the id.
Pressing any button seems to put me in a queue to talk to someone, but never seems to go thru.
I'm on the do not call list, which would be enforced by the government, excepting that the entire bureau has been gutted by the last administration. Not to worry though... when I find the location...
I spoke with my phone company and the FTC. These are crooks trying to scam people out of credit card numbers. The FTC is working on trying to shut them down. The best thing to do when you receive a call is to not answer. Do not press "1" to speak with them or "3" to 'discontinue receiving calls' since doing so lets them know that they have a live person, in which case you will receive even more calls.
If you want to register a complaint with the FTC (to encourage them or give them a better sense of how many people are affected), call 1-877-382-4357.
If you are with Qwest, dialing *57 will activate a call trace. This costs $1 and I'm not sure if it helps, but it may encourage them to put more resources into solving the problem. If nothing else, you can talk to a Qwest representative about the problem. I found them to be very helpful and informative.
Note that the scammers are spoofing their caller ID, so it is impossible to effectively block or trace them. The "truth in caller ID" act of 2010 would have prevented such nonsense, but it never became law. Search for "truth in caller ID act" to learn more.