B757 FLT CREW FLYING PUBLISHED DEPARTURE MONITORS TCAS TFC; BUT IN WAITING FOR TCAS RA; COMES WITHIN 300 FT VERTICALLY OF TFC; WAITING FOR TCAS CLIMB COMMAND.

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WE DEPARTED OFF OF RWY 31L AT BFI. CLRNC WAS NEEDLE 6 DEP WHICH STATES 'RWY HDG TO 2000 FT.' THE CAPT WAS THE PF. WE WERE IN THE PROCESS OF CLEANING UP THE ACFT AND LEVELING OFF AT 2000 FT. CLBING THROUGH APPROX 1000 FT; I NOTICED A TARGET ON THE TCAS THAT WAS DIRECTLY IN FRONT OF US AT APPROX OUR SAME ALT AND ABOUT 2.5-3 MI AHEAD OF US. THE TARGET WAS RIGHT ON OUR 'TRACK' LINE AND CLBING (UP ARROW NEXT TO ACFT SYMBOL). I WAS LOOKING OUTSIDE FOR THE TFC AND PERFORMING DUTIES CALLED FOR BY THE CAPT (SPD MODE; BUG SPD; FLAPS TO XX; ETC) AND MONITORING THE TCAS. THE TCAS WAS SET TO THE 5 MI RANGE. IT BECAME APPARENT VERY SHORTLY AFTER CLBING THROUGH 1000 FT THAT THERE WOULD PROBABLY BE A CONFLICT WITH THE TARGET DIRECTLY AHEAD. I TOLD THE CAPT ABOUT THE TFC ON THE TCAS AND WAS WAITING TO GET A WORD IN WITH THE TWR CTLR BUT DUE TO RADIO CONGESTION AND COCKPIT DUTIES; I COULD NOT. I EXPECTED A TA AND SUBSEQUENT RA MUCH SOONER THAN WE ACTUALLY GOT ONE. WE DID NOT GET A TA AT ALL. AT APPROX 1700 FT WITH THE TARGET LESS THAN 1/4 OF A MI IN FRONT OF US AND APPROX 300 FT BELOW AND STILL CLBING WE FINALLY GOT AN RA WITH A 'CLB; CLB' SHOWING A 1500-2000 FPM CLB REQUIRED. THE CAPT INITIATED THE RA MANEUVER AND I KNEW IT WAS GOING TO BE VERY CLOSE SO I WAS URGING HIM TO CLB FASTER. WE FLEW DIRECTLY OVER THE TARGET AND OUR SYMBOLS MERGED ON THE TCAS. I KNOW I SAW A '-300' AND I THINK IT EVEN WENT TO '-100' BUT I CAN'T BE SURE BECAUSE OUR ACFT SYMBOL WAS DIRECTLY ON TOP OF THE TARGET SYMBOL. I NEVER DID SEE THE TARGET ACFT VISUALLY. I THINK THAT WAS DUE TO OUR DECK ANGLE ON A VERY LIGHT WT TKOF. JUST A MOMENT BEFORE THE RA; TWR TOLD US TO SWITCH TO DEP. I WAS SWITCHING THE RADIO WHEN THE RA OCCURRED. I NOTIFIED DEP THAT WE WERE COMPLYING WITH AN RA AND CLBING. WE GOT THE 'CLR OF CONFLICT' AROUND 3000 FT AND NOTIFIED DEP. WE WERE THEN GIVEN CLB AND HDG INSTRUCTIONS. I ACKNOWLEDGED THE INSTRUCTIONS AND TOLD THEM THAT WE MISSED THE OTHER ACFT BY ONLY 300 FT. ONLY A COUPLE OF THINGS WOULD HAVE HAD TO BE DIFFERENT FOR THIS EVENT TO HAVE RESULTED IN A COLLISION. 1) IF WE HAD BEEN AT OUR NORMAL HVY WT INSTEAD OF VERY LIGHT WT (153000 LBS) OUR CLB WOULD NOT HAVE BEEN AS GOOD. 2) IF WE HAD GOTTEN THE NORMAL RR 'DEEP CUTBACK' THAT HAPPENS WHEN YOU SELECT VNAV INSTEAD OF A 'LOW ALT CAPTURE' WHICH RESULTS IN US SELECTING 'SPD' MODE AND THUS A MUCH HIGHER THRUST WE WOULD NOT HAVE CLBED AS FAST EITHER. THERE IS AN APPARENT WEAKNESS IN THE TCAS LOGIC THAT WOULD ALLOW THESE 2 ACFT TO COME THIS CLOSE BEFORE GIVING AN RA. ANOTHER CONTRIBUTING FACTOR IS THE AMOUNT OF GA TFC IN AND AROUND BOEING FIELD. THIS WOULD NOT HAVE HAPPENED AT SEA. ONE OF MY BIGGEST CONCERNS IS MY/OUR (PLTS IN GENERAL) RELUCTANCE TO TAKE EVASIVE ACTION WITHOUT HAVING AN RA ANNUNCIATION. I REMEMBER READING SOMEWHERE THAT WE ARE NOT ALLOWED TO TAKE EVASIVE ACTION BASED SOLELY ON A TA ANNUNCIATION. IN THIS INSTANCE WE NEVER HAD A TA AND IT WAS APPARENT TO ME THAT THERE WOULD BE A CONFLICT LONG BEFORE WE GOT THE RA. BUT; IF WE HAD INITIATED A CLB OR TURN WITHOUT THE RA WE COULD HAVE BEEN SUBJECT TO A VIOLATION BECAUSE WE NEVER DID SEE THE OTHER ACFT OR HAVE HIM IN SIGHT TO CORROBORATE WHAT THE TCAS WAS TELLING US. I KNOW THIS RELUCTANCE CERTAINLY SLOWED DOWN MY RESPONSE TO THE DEVELOPING SITUATION IN THOSE PRECIOUS FEW SECONDS BEFORE WE GOT THE RA.