A B757 FLT CREW TOOK OFF FROM LAS WITHOUT ATC RTE CLRNC.

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WE PREPARED ACFT FOR PUSHBACK; GOT ATIS AND SET UP DEP SID IN THE MCP OF AUTOPLT; FMC AND ALTIMETER. WE HAD A 'CANNED' RTE VIA A 'CANNED' SID FILED AND WE BRIEFED THIS SID; WHICH WAS AN RNAV SID. WE PUSHED BACK; STARTED ENGS; TAXIED TO RWY; GOT INTXN TKOF; HAD TO RE-DO TKOF DATA. FO WAS BUSY; I TAXIED THE JET. WE TOOK OFF; CLBED OUT AND CONTACTED DEP CTL. DEP TOLD US TO SQUAWK '1311' AND WHEN WE LOOKED DOWN; XPONDER WAS INCORRECTLY SET AT '1151.' DEP THEN TOLD US 'CLRED SHEAD 4 DEP; MAINTAIN 7000 FT.' WE BOTH THEN REALIZED WE HAD NOT PICKED UP OUR IFR ENRTE CLRNC. WE HAD THE PROPER (FILED) RTE SET UP IN FMC; ON AUTOPLT AND CORRECT HDGS; WHICH WE FLEW. WE HAD THE CORRECT ALT RESTR SET ALSO; FROM THE SID COMMERCIAL PLATE AND PRIOR EXPERIENCE. OUR XPONDER WAS ONLY INCORRECT BY 2 DIGITS. WE WERE RUSHED TO BLOCK OUT ON-TIME; TAXI OUT TO A DIFFERENT RWY THEN ANTICIPATE AND THEN WAS ASSIGNED AN INTXN FOR DEP. WE WERE BOTH TASK SATURATED AND MERELY FORGOT TO GET CLRNC. CONTRIBUTING WAS THE PREVIOUS 6 LEGS I HAD FLOWN WERE ALL IN EUROPE AND THE MIDDLE EAST; WHERE IFR/ENRTE CLRNCS ARE GIVEN ON TAXI OUT OR EVEN HOLDING SHORT OF RWY. SUPPLEMENTAL INFO FROM ACN 706508: THIS OCCURRED BECAUSE OF BAD CRM. CAPT BIG EGO. I AM THE CAPT. REFUSAL TO LISTEN TO FO'S REPEATEDLY PLEAD TO HELP OUT. CAPT'S FAILURE TO REALIZE THAT FO WAS OVERLOADED AND UNDER TREMENDOUS STRESS TO ACCOMPLISH BOTH WORKLOADS AND GET THE ACFT OUT ON TIME.