FO OF A B737 FAILED TO MAKE ENRTE ALT XING RESTR DUE TO DELAY IN PROGRAMMING THE ACFT FMC FOR THE NEW ALT.

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WITHIN A SPAN OF APPROX 5-7 MINS; WE HAD RECEIVED 2 CRUISE DSCNT ATC CLRNCS: 'DSND TO FL350' FROM FL370 AND 'DSND TO FL310' FROM FL350. PRIOR TO REACHING/LEVELING AT FL310; THE CAPT SWITCHED OFF THE ATC FREQ FOR THE IN-RANGE CALL TO THE COMPANY ON #2 RADIO. WHILE HE WAS OFF; I RECEIVED THE FOLLOWING CLRNC FROM ZLA; 'CROSS 50 MI NW OF DRAKE AT AND MAINTAIN FL290.' I WROTE THE CLRNC DOWN AND READ IT BACK VERBATIM. I THEN BEGAN TO ENTER THIS XING RESTR IN THE LEGS PAGE ON THE FMC/CDU. AS I WAS MAKING SURE THAT I HAD THE CORRECT RADIAL/DISTANCE/FIX INFO TYPED INTO THE SCRATCH PAD; THE CAPT CAME BACK ON THE #1 RADIO. I INFORMED HIM OF OUR CLRNC; AND HE RECOGNIZED THAT WE WERE ALREADY AT THAT XING RESTR. THE ACFT HAD LEVELED OFF AT FL310 BECAUSE I HAD NOT YET ENTERED THE XING RESTR. ATC INQUIRED ABOUT OUR ALT AND CAPT RESPONDED THAT WE WEREN'T GOING TO MAKE IT. CTLR RESPONDED THAT 'LEVELING AT FL310 WAS OUR FIRST MISTAKE.' I ENGAGED VERT SPD MODE AND EXPEDITED THE DSCNT TO FL290. CTLR HANDED US OFF TO ZAB WITHOUT FURTHER DISCUSSION; BUT WE COULD TELL HE WASN'T PLEASED. AS USUAL; SEVERAL FACTORS CONTRIBUTED TO THIS DEV. CHIEF AMONG THEM WAS THE NATURE OF THE CLRNC TO 'CROSS 50 NM NW OF DRAKE AT FL290.' THE CAPT HAD HEARD MY READBACK AND WATCHED ME ENTER FL290 ON THE MCP DESPITE BEING OFF OF THAT FREQ. BASED ON THAT; WE BOTH AGREED WE COULD NOT HAVE BEEN MORE THAN ABOUT 55-58 MI FROM DRAKE WHEN THE CLRNC WAS ISSUED; AND WE HAD NOT YET EVEN LEVELED OFF FL310.