Sounds like an at&t problem there.
Try a couple things here that may be a quick fix if not you will need to contact at&t data support tomorrow.
1. Reboot iPhone - Now test voicemail
2. Settings - Airplane Mode - Turn ON for 1 min then turn off - Test voicemail once it reacquires service
3. Settings - General - Reset - Reset Network Settings - Allow iPhone to reboot - try voicemail
4. Settings - General - Network - Turn 3G off and test VM, turn back on test again
5. Remove SIM card and put back in and retest
http://support.apple.com/kb/HT1438
Are you able to go to Keypad in telephone, hold down the 1 key. Does it dial into voicemail?
Are you able to use any other internet services on iPhone?
If none of these steps work contact either at&t support or apple iphone support who can get you in touch with proper at&t data support group to assist with voicemail troubleshooting over the network.