FLC OF B737-300 HAS CONFLICT WITH AN SMA WHEN UNDER ABQ CTL. TCASII RA ALERTS THE FLC JUST AS ATC GIVES TA.

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ON THE FRIH03 ARR WE WERE CLRED TO DSND TO I BELIEVE 8000 FT. ATC VECTORING US; AND A FAIR AMOUNT OF TFC (SAME VFR) NEAR THE N END OF ALBUQUERQUE. I CAUGHT SIGHT OF ONE TARGET ON TCASII AT 11 O'CLOCK POS AND ABOUT 3 MI; THAT LOOKED LIKE A POTENTIAL CONFLICT. WE WERE CLRED DOWN THROUGH HIS ALT; AND APPEARED TO BE CONVERGING. I WATCHED HIM FOR A COUPLE OF SECONDS; AND THEN TOLD MY FO TO LEVEL OFF UNTIL WE PASSED THAT TARGET. I HAD MY TCASII IN BELOW/RELATIVE; SO I CAN'T SAY WHAT HIS MSL ALT WAS FOR SURE. WE STARTED TO LEVEL OFF; AND ALMOST SIMULTANEOUSLY GOT A TA FROM ABQ APCH AND A TCASII 'TFC; CLB; CLB' RA. MY FO WAS FOLLOWING THE RA; AND CALLED APCH TO TELL THEM WE WERE CLBING TO FOLLOW THE TCASII RA. APCH APOLOGIZED FOR THE LATE TFC CALL (HE WAS QUITE BUSY AT THE TIME). THE TFC APPEARED TO BE VFR. APCH SAID THE TFC APPEARED TO START CLBING UNEXPECTEDLY. OUR CLOSEST RELATIVE ALT WAS ABOUT 300 FT AT ABOUT 1 MI; AND 700 FT VERT AS WE CROSSED ALMOST DIRECTLY OVER HIM. WITHOUT TCASII RA; I ESTIMATE WE WOULD HAVE COME WITHIN 200 FT VERTLY AND ABOUT 100 YARDS OFF HIS NOSE. I ACQUIRED THE TFC VISUALLY AT ABOUT 1/2 MI; EVEN THOUGH I KNEW WHERE TO LOOK FROM THE TCASII DISPLAY. WHILE I THINK WE WOULD HAVE MISSED; IT WOULD HAVE BEEN VERY CLOSE. THANK YOU; TCASII.