EMB145 HAS MULTIPLE TCASII TA'S AND RA'S IN CLASS B AIRSPACE.

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WE WERE LEVEL AT 6000 FT ON A VECTOR S OF SAX VOR AND NW OF EWR. NEW YORK APCH WAS VERY BUSY. AT ABOUT THE SAME INSTANT; 2 THINGS HAPPENED: 1) WE GOT A TA ON A TARGET AT OUR 1 O'CLOCK POS AND 300 FT BELOW US. 2) CTLR GAVE US A 40 DEG TURN TO THE L. THE TARGET HAD NO CLB VECTOR WHICH MADE ME THINK THAT HE WAS LEVEL. AS WE ROLLED INTO THE TURN; I TOLD THE FO (PF) TO BE READY TO CLB. I TRIED TO ASK THE CTLR ABOUT THE TARGET; BUT AS WE WERE TURNING WE GOT AN RA TO DSND. I WAS SO BUSY LOOKING FOR THE TFC OUTSIDE; MONITORING THE L TURN; AND LISTENING TO THE RADIO THAT I DID NOT REALIZE THE TARGET WAS ACTUALLY SLOWLY CLBING! AS A RESULT; I THOUGHT THE TCASII WAS IN ERROR. I TOLD THE FO NOT TO DSND. BY NOW WE WERE ROLLING OUT FROM THE TURN AND WE WERE STILL LOOKING FOR THE TARGET WHEN THE TCASII SAID 'XING DSND; XING DSND.' ONLY NOW DID I REALIZE THAT THE TARGET WAS CLBING. AT THAT INSTANT I TOLD THE FO TO DSND AND WE BOTH SAW THE TARGET -- A C182RG OR C210. COULD NOT TELL WHICH; BUT IT WAS CLOSE! WE WERE IN A STEEP DSCNT ABOUT 500 FT BELOW OUR ASSIGNED ALT WHEN THE CTLR TOLD US TO MAINTAIN 6000 FT BECAUSE HE HAD A B777 TFC BEHIND; BELOW AND SOME DIRECTION TO US. I LOOKED OUT MY L WINDOW AND SAW HIM THERE -- LESS THAN 1 MI AWAY; MOST LIKELY AT 5000 FT. I TOLD THE CTLR ABOUT THE CESSNA AND HE DID NOT REPLY. I THINK THAT IF THE CTLR WAS NOT SO OVERLOADED; HE COULD HAVE POINTED OUT THE CESSNA. I PROBABLY SHOULD HAVE FOLLOWED THE RA IMMEDIATELY; BUT IT'S A DIFFICULT THING TO BLINDLY FOLLOW WHAT THE TCASII COMPUTER TELLS YOU. SINCE THE LAST TCASII DISPLAY I SAW SHOWED THE CESSNA 300 FT BELOW US WITH NO CLB VECTOR; I THINK THE CONFUSION OF TURNING; TALKING TO THE CTLR; TALKING TO MY FO; AND LOOKING FOR THE TFC VISUALLY CAUSED ME TO HAVE TUNNEL VISION.