ACR CREW MISSES XING RESTR BY DEPENDING ON FMS TO FIGURE OUT THE DSCNT.

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CLRNCS TO FL270; FL240; FL200 THEN CROSS 10 MI W PHK AT 10000 FT. AUTOPLT ENGAGED WITH FMS. XING RESTR ENTERED; VNAV ENGAGED AND ANNUNCIATED. NO TOP OF DSCNT EVER SHOWED -- EITHER ON CRT OR IN CRUISE OR DSCNT PAGE ON CDU/FMS. BEGAN FORCED DSCNT USING AUTOPLT VIA FMS DSND NOW MODE. TREND LINE SHOWED ON SCHEDULE TO MAKE XING. ZMA GAVE RESTR A LITTLE LATE; BTWN LLAKE AND CHAOS INTXNS. CTR ASKED IF WE WERE GOING TO MAKE XING. INSTINCTIVELY I SAID YES; THEN REALIZED DISTANCE TO GO WAS VERY SHORT AND READVISED ZMA. AT THAT POINT I CLICKED THE AUTOPLT OFF. IMMEDIATELY THE TREND LINE WAS OFF THE SCALE. PULLING THE THROTTLE TO IDLE AND DEPLOYING THE SPD BRAKES WAS THE ONLY OPTION. I CONFESS; I RELIED TOO MUCH ON THE FMS AND DID NOT MENTALLY BACK IT UP (I WILL FROM NOW ON) TO ASSURE MAKING THE RESTR. CTR DID ISSUE THE XING LATE; BUT HAD I CAUGHT IT AT THAT TIME; I MIGHT HAVE MADE IT; THOUGH STILL DEPLOYING SPD BRAKES CROSSED THE WAYPOINT 4000 FT HIGH. ATC DIDN'T COMMENT AND SEEMED TO BE SATISFIED BY OUR RATE OF DSCNT; AFTER WE INFORMED HIM WE WEREN'T GOING TO MAKE THE RESTR. SUPPLEMENTAL INFO FROM ACN 470856: MEANWHILE; I (THE FO) WAS PICKING UP ATIS ON COM #2. I NOTIFIED THE CAPT I WAS OFF OF COM #1 (ATC). IT TOOK A COUPLE OF TIMES TO GET ATIS DUE TO PICKING IT UP 1/2 WAY AND BEING THERE WERE NUMEROUS NOTAMS. THE FMS PROGRAMMING PART AND THE LATE DSCNT AND NO PRINTED ATIS ALL ADDED UP TO A VERY BUSY TIME. IF I HAD PRINTED ATIS I WOULD NOT HAVE TO LISTEN 2 1/2 TIMES TO ATIS IN A BUSY SIT; WHICH WOULD ALLOW ME MORE TIME TO DOUBLECHK THE PF'S PROGRAMMING.