A B757-200 AND B737-300 HAD LESS THAN LEGAL SEPARATION ON THE SID AT SJC.

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THE COPLT ASKED ME TO CALL OUT THE 1.8 FIX ON THE LOOPE 9 DEP SO HE COULD HAVE A BACKUP TO MAKE THE TURNOUT. AFTER RAISING THE GEAR ON TKOF; I SAID 'LOOKING FOR 1.8.' HE THOUGHT I WAS MAKING THE CALLOUT HE HAD ASKED ME TO MAKE AND STARTED THE R TURN. THE ACFT HAD DRIFTED SLIGHTLY L OF TRACK SO I MISTAKENLY THOUGHT HE WAS CORRECTING BACK AND FAILED TO TELL HIM TO HOLD THE TURN UNTIL 1.8. BY THEN; WE HAD ACTUALLY TURNED ABOUT 45 DEGS AND RECEIVED A TCASII TA ON THE ACR FLT WHICH HAD DEPARTED AHEAD OF US AND I HAD A VISUAL ON ACR AT THIS TIME. WE FLEW BEHIND ACR ABOUT 2 NM. WE MADE A DEP ERROR DUE TO MY POOR COM WITH THE COPLT AND SLOW REACTION TO HIS ACTION. BELIEVE I WAS SLOW DUE TO THE EARLY HR AND LACK OF SLEEP DUE TO A HEAD COLD. SUPPLEMENTAL INFO FROM ACN 525637: LOUPE DEP FROM SJC. I HAD BRIEFED THE CAPT TO CALL OUT THE 1.8 SJC DME TO BACK UP MY TURN POINT; AS I HAD SELECTED 'LNAV' AT 4000 FT AGL. AFTER TKOF; I HEARD THE CAPT SAY '1.8.' IT LOOKED EARLY; BUT I HAD COMMENCED MY TURN. AS WE CAME THROUGH ABOUT 030 DEGS MAGNETIC; WE GOT A TA; AND THE TWR CALLED OUT TFC TO US; WHICH WE HAD ATTAINED VISUALLY. WE PASSED BEHIND THE B737; WHICH HAD DEPARTED BEFORE US; BY APPROX 2 NM; AND BELOW THEM. THESE ERRORS OCCURRED FOR THE FOLLOWING REASONS: 1) I HAD NEVER FLOWN THIS DEP; WHICH BECOMES BUSY NOT BECAUSE OF THE TURN; BUT ALSO THE SPD/ALT RESTRS. 2) I HAD MISTAKEN THE CAPT'S '1.8' CALL FOR THE TURN POINT; NOT AS A REMINDER. EVEN THOUGH IT DID NOT 'FEEL' RIGHT TO TURN AT THIS TIME; I KNEW THE CAPT AND TRUSTED HIS JUDGEMENT IMPLICITLY. I SHOULD HAVE ASKED; BUT A FURTHER RESTR (TURN INSIDE 4 DME) SHADED MY JUDGEMENT. AT NO TIME WAS IT LIKELY THAT OUR ACFT WOULD CROSS FLT PATHS WITH THE B737. EVEN IN IMC; THE TA AND CTLR ACTION WOULD HAVE PRECLUDED THIS. SUPPLEMENTAL INFO FROM ACN 525641: CAPT FLEW FLAWLESS SJC 8 DEP (TURNED AT 1.8; DID NOT EXCEED 4.0. BROKE OUT ABOUT 1500-2000 FT MSL. IN R TURN TO 110 DEGS; I LOOKED BACK TOWARDS SJC TO SEE AN ACFT COME OUT OF THE CLOUDS. THE ACFT APPEARED TO BE IN A R BANK AND CLBING; ON A CONVERGING COURSE. AS WE INTERCEPTED THE OAK 121 DEG RADIAL PASSING APPROX 4000 FT; IT BECAME APPARENT TO ME THE ACFT WAS NOW ON A COLLISION COURSE. I POINTED THIS OUT TO THE CAPT. BAY DEP GAVE US A CLB TO 15000 FT AND I RECOMMENDED WE EXPEDITE. WE RECEIVED A TA. BAY DEP ASSIGNED A HDG OF 090 DEGS (30 DEGS L) FOR TFC. WE WERE PASSING 5000 FT; ESTABLISHED ON THE OAK 121 DEG RADIAL. I ADVISED BAY WE HAD THE TFC IN SIGHT AND WERE GOING TO ESCAPE STRAIGHT AHEAD. MY GUESS IS THAT THE ACFT RECEIVED A TA/RA THE SAME TIME WE DID. BY THE TIME BAY TRIED TO TURN US; THE ACFT HAD BEGUN A L BANK TO PASS BEHIND US. HAD I NOT MAINTAINED VISUAL; AND TOOK BAY'S VECTOR; WE WOULD HAVE TURNED INTO THE ACFT'S ESCAPE MANEUVER. BAY ADVISED WE MAINTAIN VISUAL SEPARATION AND PROCEED ON COURSE. THE ACFT MADE ITS FIRST XMISSION. ACKNOWLEDGED TFC (US) AND PASSED BEHIND AND BELOW (APPROX 1/2 NM; 500 FT).