B757 EXPERIENCED TFC CONFLICTION WITH TFC UNDER N90 CTLR WHILE ON N90 FREQ IN JFK CLASS B AIRSPACE.

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DEP CTL WAS VERY BUSY. OUR FLT WAS CLRED TO CLB TO 7000 FT. DURING THE CLB THROUGH 5000 FT; WE SPOTTED TCASII TFC AT 1 O'CLOCK POS; 3 MI. IT APPEARED TO BE LEVEL AT 6500 FT; AT WHICH TIME WE RECEIVED A TCASII TA. CAPT DECREASED THE CLB RATE TO 500 FPM AS WE ATTEMPTED TO QUERY ATC. UNABLE TO BREAK INTO ATC COMS; THE CAPT ELECTED TO LEVEL OFF AT 6000 FT AND SPOT THE TFC VISUALLY. THE FO AND CAPT VISUALLY VERIFIED THE SINGLE ENG ACFT AND WATCHED IT PASS IN FRONT OF OUR FLT PATH. ATC CHIMED ON WITH A TURN COMMAND TO BOTH ACFT. AS WE TURNED TO THE R; THE SMALL CRAFT PASSED OFF OUR L SIDE 500 FT ABOVE AND 1 1/2 MI LATERAL SEPARATION. BASED ON THE CLOSURE RATE THIS CAPT BELIEVES THAT; HAD HE CONTINUED TO CLB TO 7000 FT; WE WOULD HAVE RECEIVED AN RA AND BEEN COMMANDED TO CLB AT AN INCREASED RATE TAKING US THROUGH OUR ASSIGNED ALT OF 7000 FT. AT NO TIME WAS THIS EVENT NOTICED BY THE PAX OR WAS ANY EVASIVE ACTION TAKEN OR NECESSARY. THIS CAPT WOULD PREFER NOT TO BE PLACED IN A POS OF CLBING THROUGH A VFR ACFT ALT IN SUCH A BUSY ENVIRONMENT. HE IS HAPPY WITH THE OUTCOME BUT CAN SEE THE POSSIBILITY FOR A WORSENING SIT HAD THE EVENT BEEN HANDLED DIFFERENTLY.