CARJ ON VECTORS FOR VISUAL APCH TO CVG EXPERIENCED TCASII RA WITH PRECEDING TFC.

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ARR WAS FROM S ON SWEED7. WE WERE TOLD TO EXPECT RWY 18L. STANDARD VECTORS WERE ISSUED FOR THE L DOWNWIND. THE APCH CTLR GAVE US A DSCNT ABEAM THE ARPT AND TOLD US IT WOULD BE A SHORT APCH. HE THEN HANDED US OFF TO THE FINAL CTLR. THE FINAL CTLR GAVE US A 'SLOW TO 170 KTS AND THEN L TURN 270 DEGS.' WE WERE ALREADY AT 170 KTS AND WE MADE THE TURN TO 270 DEGS. WE WERE NOW ON BASE LOOKING AT THE FINAL. THE CTLR THEN STARTED CALLING TFC THAT WAS ON THE FINAL. THE STATEMENT WAS 'FAST MOVING TFC R TO L AT THE 2 O'CLOCK POS.' BOTH THE FO AND I SAW THE TFC; BUT WE DECIDED NOT TO CALL IT BECAUSE OF THE SPACING. WE DID NOT WANT TO FOLLOW TFC THAT WOULD BE ARRIVING AT THE SAME POINT ON THE FINAL AT THE SAME TIME AS US. IN ADDITION; WE WERE HEADED DIRECTLY AT THIS ACFT ON FINAL WITH A PRETTY GOOD CLOSURE RATE AND I WAS ANTICIPATING ANOTHER TURN TO THE R FOR SOME MORE SPACING. THE CTLR CALLED THE TFC AGAIN WITH A VERY CONCERNED TONE IN HIS VOICE. IT APPEARED THAT THIS PLAN FOR TFC SEPARATION WAS BASED ON US CALLING THE TFC AND TAKING CARE OF THE SEPARATION OURSELVES. UNFORTUNATELY; WE SAW THAT THE CTLR WAS PUTTING US INTO A PRECARIOUS POS THAT WOULD REQUIRE SOME SPECIAL MANEUVERING TO AVOID A LOSS OF SEPARATION. WE DID NOT WANT TO CALL THE TFC AND BE PUT IN THAT SIT. I BELIEVE IT WAS HIS THIRD TFC CALL TO US WITH A FRANTIC TONE THAT HE SAID 'TFC 12 O'CLOCK POS.' I MADE THE COMMAND DECISION TO CALL THE TFC AND BEGIN MANEUVERING TO REMOVE OURSELVES FROM THIS SIT. AS I WAS CALLING THE TFC; WE RECEIVED A TCASII ALERT AND I INFORMED THE CTLR THAT WE WOULD HAVE TO TURN TO THE R BEFORE WE COULD TURN L TO JOIN THE FINAL. FORTUNATELY; WE ONLY WEIGHED 36K FOR LNDG; SO WE HAD SLOW MANEUVERING SPDS. WE COULD NOT GO WIDE BECAUSE OF THE FINAL TO RWY 18R. WE COULD NOT TURN R VERY FAR BECAUSE OF OTHER TFC ON FINAL TO RWY 18L. WE HAD TO CONFIGURE TO LNDG IMMEDIATELY TO BE ABLE TO SLOW DOWN AND IT REQUIRED S-TURNS TO THE L OF THE FINAL TO GET OUR SPACING BACK. IT TASKED BOTH ME AND THE FO WITH A VERY HIGH WORKLOAD IN FLYING AND AVOIDING TFC. I AM CURIOUS WHAT THE PLAN WAS IF WE WOULD NOT HAVE CALLED THE TFC. IT DID APPEAR THAT A BACK-UP PLAN EXISTED. THE CTLR WAS VERY BUSY AND THE FREQ WAS CONGESTED AT THE TIME. I AM NOT SURE WHAT PRESSURE HE WAS UNDER AT THE TIME. WE GOT A LATE HDOF TO THE TWR AND HE LET US KNOW THAT WE HAD 3 MI ON THE TFC AT THAT TIME.