PLT OF SMA ACFT TOOK EVASIVE ACTION FROM A CLBING ACR ACFT.

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WHILE DSNDING FOR LNDG AT BNA; I WAS NOTIFIED OF JET TFC. I RPTED THIS TFC IN SIGHT AND WAS TOLD TO MAINTAIN VISUAL SEPARATION. I ACKNOWLEDGED THIS AND CONTINUED MY APCH TO DOWNWIND TO RWY 2L. THE TFC; WHICH HAD JUST DEPARTED RWY 31 WAS NOT CLBING AS FAST AS I HAD ANTICIPATED AND THEREFORE; I INCREASED MY RATE OF DSCNT TO AVOID A CONFLICT. AS THE TFC CAME NEARER; IT STILL APPEARED TO BE A CONFLICT AND I SOMEWHAT ABRUPTLY PUSHED FORWARD ON THE YOKE AND REDUCED PWR TO AVOID IT. IT WAS TOO LATE TO SAFELY INITIATE ANY TURN THAT WOULD HAVE AVOIDED A CONFLICT AND A RAPID INCREASE IN DSCNT RATE WAS MY ONLY RECOURSE. IT DID NOT APPEAR TO ME THAT THE TFC MADE ANY ATTEMPT TO ALTER ITS COURSE OR RATE OF CLB TO AVOID ME. I ESTIMATE THAT THE JET PASSED 500 FT ABOVE AND APPROX 300 FT LATERALLY FROM ME. THE JET THEN MADE AT LEAST 2 RADIO TRANSMISSIONS TO THE TWR COMPLAINING OF 'THAT BEING WAY TOO CLOSE' AND STATING THAT HIS TCASII HAD INDICATED ONLY 100 FT SEPARATION. THE CTLR INFORMED HIM THAT I WAS MAINTAINING VISUAL SEPARATION FROM HIM AND THE PLT THEN STATED THAT 'HE HAD 150 PEOPLE IN THE BACK THAT WAS WAY TOO CLOSE.' A SHORT TIME LATER; THE JET WAS GIVEN A FREQ CHANGE TO DEP. I THEN XMITTED 'WHY DON'T YOU STAY IN DALLAS.' ALTHOUGH THIS WAS AN UNNECESSARY COMMENT ON MY PART; IT DID EXPRESS MY FEELINGS AT THE TIME. THIS PARTICULAR AIRLINE CREW CERTAINLY SHOWED NO CONCERN FOR THEIR '150 IN BACK' UNTIL AFTER WE HAD PASSED. EITHER THEY DID NOT SEE ME OR ASSUMED THAT I WOULD DO WHATEVER WAS NECESSARY TO AVOID THEM (LUCKILY THEY WERE CORRECT). I HAVE BECOME QUITE CONCERNED RECENTLY THAT CREWS OF TCASII-EQUIPPED ACFT ARE USING IT AS A CRUTCH AND FAILING TO DILIGENTLY LOOK OUTSIDE THE ACFT FOR TFC. IN DEFENSE OF THE CREW; NEITHER OF US SHOULD HAVE BEEN PUT IN THIS SITUATION TO BEGIN WITH. WHETHER THEY SHOULD NOT HAVE BEEN ISSUED TKOF CLRNC UNTIL I HAD CLRED THE DEP END OR RWY 31 OR I SHOULD HAVE BEEN TOLD TO MAINTAIN 2500 FT WHILE THEY WERE HELD TO 2000 FT UNTIL WE HAD PASSED. IF I HAD IDENTED THE WRONG ACFT 'IN SIGHT' OR HAD MY ATTN DIVERTED FOR A FEW SECONDS AFTER FIRST SIGHTING THE TFC; THIS COULD HAVE EASILY RESULTED IN A COLLISION.