MD88 AT FL330 EXPERIENCED TCASII RA WHILE ON ATC VECTORS AND CLBING TO FL350.

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ON A VECTOR AT FL330 FOR TFC WHEN ATC ASKED IF WE COULD CLB TO FL350. WE SAID YES; WERE GIVEN CLRNC TO FL350. WE ACKNOWLEDGED THE CLRNC. THEN ATC SAID WE NEEDED TO BE AT FL350 IN 1 1/2 MINS. WE RESPONDED WITH 'WE WILL DO THE BEST WE CAN.' ATC THEN GAVE US A R TURN. WE READ BACK THE TURN AND TOLD ATC WE WOULD NOT MAKE THE RESTR. WE GOT A TA ON TCASII THAT WENT TO RA. TCASII INSTRUCTED A CLB SO I AS PF SACRIFICED AIRSPD AND INCREASED THE RATE OF CLB. WE WERE AT FL335. AT THAT TIME ATC ASKED IF WE WERE AT FL350. WE RESPONDED 'NO' AND REPEATED THAT WE TOLD THEM WE WERE NOT ABLE TO MAKE THE RESTR. NO RESPONSE FROM ATC. PA TERMINATED. VECTORED BACK ON COURSE. SUPPLEMENTAL INFO FROM ACN 609014: IN CRUISE AT FL330; WE WERE GIVEN A 40 DEG L TURN FOR TFC. 20-30 SECONDS LATER; WE WERE GIVEN A TURN 30 DEGS R. AFTER 10 SECONDS LATER; WHEN IT WAS APPARENT THE TURN HAD KILLED OUR CLB RATE; WE TOLD THEM WE WOULD BE UNABLE TO MAKE FL350 IN THE TIME HE REQUESTED; WE WERE GIVEN A FURTHER TURN. I THINK ONE WAY A SIT LIKE THIS COULD BE AVOIDED IS BY THE CTLR ASKING IF YOU WILL BE ABLE TO MEET ANY TYPE OF PERFORMANCE CRITERIA HE HAS BEFORE ISSUING A CLRNC. WHEN CLRNC IS ISSUED WITH STIPULATIONS; BY THE TIME A PLT REALIZES HE IS UNABLE TO COMPLY; RADIO CONGESTION MAY NEGATE HIS ABILITY TO COMMUNICATE THAT INFO TO THE CTLR IN A TIMELY MANNER.