B767 FLC (ACFT X) DID NOT ADHERE TO THE TIME RESTR ISSUED BY THE CTLR TO REACH THEIR ALT. CTLR HAD TO TAKE ACTION TO KEEP BOTH ACFT X AND ACFT Y SEPARATED.

Narrative

FLYING AT FL390; THE CAPT ASKED ME TO REQUEST FL410. UPON REQUESTING; THE CTLR ASKED HOW LONG IT WOULD TAKE TO CLB THERE. I SAID 4 MINS; BUT THE CAPT CORRECTED ME AND SAID TO SAY 3 MINS. THE CTLR GRANTED THE REQUEST; ASKING WE TAKE 3 1/2 MINS. AT 2 1/2 MINS; THE CTLR ASKED IF WE WERE GOING TO MAKE IT. I LOOKED AT THE CAPT AND HE NODDED YES; SO I TOLD THE CTLR YES. WE WERE AT FL395. AT 3 MINS AND FL400; I TOLD THE CAPT WE NEEDED 2000 FPM CLB TO MAKE IT. HE SAID/DID NOTHING TANGIBLE. AT 3 MINS 20 SECONDS AND FL402; I TOOK IT ON MYSELF TO TELL ATC WE WEREN'T GOING TO MAKE IT. HE GAVE US A TURN TO THE R APPROX 50 DEGS; AND ANOTHER ACFT GOING IN THE OPPOSITE DIRECTION A TURN R (AT FL390) OF 40 DEGS. THE CAPT USED 10 DEGS OF BANK FOR A TURN. I TOLD HIM THAT WAS NOT ENOUGH. THE CTLR THEN CAME BACK AND ASKED US TO TURN FASTER; WHICH CAUSED ME TO RE-EMPHASIZE MY COMMENT TO THE CAPT ABOUT HIS TURN. WE STAYED LEVEL AT FL402 DURING THE TURN; AND OBSERVED THE ACFT AT FL390 (ON TCASII) COME WITHIN APPROX 5 MI. NO TCASII ALERT WAS GIVEN; NOR DID ATC SAY WE LOST SEPARATION. I DO; HOWEVER; FEEL THE CAPT WAS NOT PROACTIVE IN COMPLYING WITH ATC'S REQUESTS; AND MAYBE RATHER THAN STRONG URGING; I NEEDED TO ASSUME COMMAND DURING THE CRITICAL PHASES. I CERTAINLY LEARNED A LESSON IN ALLOWING A CAPT TO POSSIBLY GO TOO FAR.