TCASII PREVENTS AN NMAC IN LGA CLASS B AIRSPACE.

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THE CAPT WAS THE PF AS WE WERE BEING VECTORED FOR THE ILS RWY 22 AT LGA. WE WERE GIVEN A FINAL INTERCEPT HDG AND TOLD TO MAINTAIN 3000 FT. IN THE TURN; I WAS SCANNING FOR TFC. AFTER BECOMING ESTABLISHED ON THE INTERCEPT HDG; WE RECEIVED AN RA FOR AN IMMEDIATE CLB. I LOOKED AT THE TCASII AND SAW A TFC SYMBOL AT -100 FT. TO COMPLY WITH THE RA; THE CAPT INITIATED A PULL-UP OF APPROX 2500 FPM (WHILE ASKING FOR 'MAX PWR'). WE HAD NO VISUAL CONTACT WITH THE ACFT. AT THIS TIME; THE CAPT ALSO HEARD A CLRNC FROM APCH CTL TO CLB TO 4000 FT. I MADE 1 ATTEMPT TO CALL THEM ABOUT OUR ACTIONS WITH NO REPLY. I WAS DELAYED IN A FOLLOW-UP CALL DUE TO SCANNING FOR TFC AND FLT PATH MONITORING DUTIES. I THEN LOOKED UP AND AT OUR 12 O'CLOCK POS SAW JET TFC MOVING R TO L ABOUT 1000 FT ABOVE US AND NOW DIVERGING. ONCE WE VISUALLY VERIFIED THERE WAS NO CONFLICT WITH THIS TFC; AND IN ORDER TO COMPLY WITH OUR PREVIOUS INSTRUCTION OF LOC INTERCEPT; AND TO REMAIN CLR OF UNKNOWN AIRSPACE AHEAD; THE CAPT INITIATED A TURN OF APPROX 15 DEGS BEHIND THE JET TFC. ONCE LEVEL AT 4000 FT; THE CAPT CALLED FOR 'AUTOPLT ON' AND I AGAIN CALLED APCH CTL WITH NO RESPONSE DUE TO FREQ CONGESTION. AFTER A SECOND ATTEMPT TO CONTACT ATC; WE WERE INSTRUCTED TO TURN R HDG 360 DEGS AND MAINTAIN 4000 FT. THE CAPT THEN INITIATED A R TURN (30 DEG BANK) TO THE NEW HDG; AT WHICH POINT WE WERE GIVEN A FREQ CHANGE TO ANOTHER CTLR. HE THEN GAVE US VECTORS BACK AROUND FOR ANOTHER ILS APCH; WHICH PROCEEDED WITHOUT INCIDENT. WE SURMISED THAT THE TFC FROM BELOW COULD HAVE BEEN A VFR ACFT IN A CLB PLANNING TO LEVEL OFF UNDER THE OVERLYING AIRSPACE. THE FLOOR OF CLASS B AIRSPACE IN THE AREA VARIES FROM 1500 FT TO 3000 FT. IT WOULD SEEM TO ME TO BE NECESSARY TO LOWER THIS AIRSPACE IN THE AREA OF THE EXTENDED CTRLINE OF RWY 22; AS THIS OBVIOUSLY IS A VERY SERIOUS THREAT TO AIRLINE SAFETY. ACCORDING TO A FLT ATTENDANT SPOKEN TO AFTER THE FLT WHO WAS IN THE REAR OF THE ACFT DURING THE INCIDENT; SEVERAL PAX SAW A 'LIGHT PLANE' IN CLOSE PROX JUST BELOW AND BEHIND OUR R WING AFTER WE HAD INITIATED THE PULL-UP. THE TCASII WAS AN EXCELLENT TOOL IN HELPING US AVOID A POTENTIALLY DEADLY SIT.