A320 FLT CREW DEPART MIA PRIOR TO RECEIVING THE CORRECT WT AND BAL FIGURES FOR THE ACTUAL LOAD.

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MIAMI STATION PERSONNEL LOADED ACFT AND LOAD MASTER GENERATED COMPUTER WT AND BAL SCHEDULE WHICH HE PRESENTED ABOUT 10 MINS BEFORE DEP TIME. WE ANTICIPATED A FULL LOAD OF PAX (150) AND THEIR BAGGAGE AND 120 LBS OF CARGO. MOST OF THE BAGS WERE LOADED IN AFT CARGO; RESULTING IN A CTR OF GRAVITY AT THE AFT LIMIT WITH 150 PAX AND NO PROVISION FOR LESS THAN 150 PAX AND REMAINING WITHIN AFT CTR OF GRAVITY LIMIT. AT 1 MIN BEFORE DEP; FLT ATTENDANT #2 BROUGHT PAX COUNT TO FLT DECK SHOWING 197 PAX PLUS 1 INFANT. WE PUSHED BACK AND CALLED IN THE CHANGE IN THE PAX COUNT; BUT NO ONE ANSWERED THE RADIO. I TOLD THE TUG DRIVER ON THE HEADSET WHAT OUR COUNT WAS AND HE SAID HE WOULD TELL THE LOAD MASTER AND OR OPS. MIA STATION HAS A HISTORY OF COMS PROBS; AND IS POOR STAFFED. WE DIDN'T REALIZE THAT OUR 147 PAX COUNT DID NOT HAVE A WT AND BAL SOLUTION ON OUR COMPUTERIZED DOCUMENT AS IT NORMALLY WOULD HAVE; AND WE TOOK OFF. AFTER INITIAL CLB; I REALIZED THE PROB AND PERFORMED A MANUAL WT AND BAL CALCULATION SHOWING US WITHIN THE AFT LIMIT AND UPON ARR AT DEST; FAXED THE SAME TO MIA STATION. I THEN MADE REPEATED ATTEMPTS TO CALL ON THE PHONE AND FINALLY TALKED WITH A STATION EMPLOYEE AT ABOUT XA09 EDT; ALMOST 12 HRS LATER; TO BE SURE THEY GOT THE WT AND BAL PAPERWORK. THE EMPLOYEE THEN RECORDED THE RADIO REVISION WHICH SHOULD HAVE BEEN RECORDED BEFORE TKOF.