C560 FLT EXPERIENCED TCASII RA AT 3000 FT DURING VECTORS FROM N90; LNDG MMU.

Narrative

WHILE BEING VECTORED BY NEW YORK APCH CTL FOR THE TEB VOR/DME A APCH; WE WERE INSTRUCTED TO DEPART SBJ ON A HDG (040 DEGS?). AT OUR ASSIGNED ALT OF 3000 FT; TCASII ISSUED A TFC ALERT. ON THE TCASII DISPLAY; I NOTICED TFC AT APPROX 2 O'CLOCK POS; 2 NM; 300 FT (I CAN'T REMEMBER ABOVE OR BELOW) AND CLOSING. SHORTLY THEREAFTER; TCASII ISSUED AN RA OF 'CLB; CLB; CLB.' I IMMEDIATELY DISCONNECTED THE AUTOPLT; ADDED PWR; AND INITIATED A CLB AT THE TARGET RATE. I INSTRUCTED MY FO TO NOTIFY ATC THAT WE WERE CLBING FOR AN RA. DUE TO FREQ CONGESTION; I'M NOT SURE THAT ATC HEARD OUR XMISSION; THOUGH I DID HEAR THE CTLR INSTRUCT WHAT I BELIEVE TO BE THE OTHER ACFT: 'I REALLY NEED YOU TO CONTINUE YOUR DSCNT TO 2500 FT NOW;' OR SOMETHING TO THAT EFFECT. I STOPPED THE CLB AT 3600 FT AS TCASII INFORMED US THAT WE WERE 'CLR OF CONFLICT;' AND DSNDED BACK TO OUR ASSIGNED ALT OF 3000 FT. I INSTRUCTED THE FO TO INFORM ATC THAT WE HAD CLBED TO 3600 FT FOR AN RA; THOUGH THE FO DID NOT USE THE TERM 'RA.' INSTEAD; THE FO USED THE TERM 'TFC CONFLICT.' THE CTLR RESPONDED BY SAYING; 'YOU GOTTA DO WHAT YOU GOTTA DO.' THE REMAINDER OF THE FLT PROCEEDED UNEVENTFULLY TO TETERBORO. I AM NOT CERTAIN OF AN ACTUAL MISS DISTANCE; BUT WAS GLAD TO HAVE TCASII. NOT ALL OF OUR ACFT HAVE TCASII INSTALLED. I BELIEVE THAT THE OTHER ACFT'S DELAYED COMPLIANCE WITH ATC'S DSCNT INSTRUCTION COUPLED WITH VERY CONGESTED AIRSPACE AND AN EXTREMELY BUSY CTLR CONTRIBUTED TO THIS EVENT.