I got one late last week as well.  I have Verizon so this is not AT&T related. I did not receive a text message but the voicemail was pretty much exactly as you said.  It says the mailbox is full and cannot accept new messages at this time when you call them back.  Annoying.  I was heading out for a trip and certainly didn't need problems with my card.

Recieved a message that my credit card has been deactivated and I should call DMO4690296 to reactivate my credit card.

"This is Finance Center Federal Credit Union. Your card has been deactivated. To reactivate your card, call (418) 615-3159 and note number..." Fraud!

Got 2 calls this morning on my AT&T cell phone too. Card deactivation from Central National Bank of Enid. Called the actual bank in Enid, OK. Definitely a phishing scam

Also got the message today around 1130am, "This is Security National Bank, your card has been deactivated, please call the security department at (418) 615-3159 to reactivate your card, note (either) 418153159", or "1816153159", I couldn't catch what the message was saying. I have AT&T too. Look up the phone number and it's a definately a scam.

Got a call about 40 mn ago on AT&T home phone.  Supposed problems with (nonexistent) card at Financial Center Credit Union.