CARJ RECEIVES EGPWS TERRAIN WARNING WHEN REQUIRED TO MAINTAIN 6500 MSL AFTER TKOF FROM DEN.

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WE DEPARTED RWY 17R IN VMC IN DENVER. ORIGINAL CLRNC WAS FOR 19000 FT BUT TKOF CLRNC WAS 7000 FT AND RWY HDG. AFTER CAPT TOOK OFF; WE WERE ALERTED TO AN AIRBUS THAT TOOK OFF RWY 25; HAD TURNED ABOUT 270 DEGS L AND WAS GOING TO CROSS OUR PATH ABOVE US. AFTER I CALLED ACFT IN SIGHT; TWR ASSIGNED A LEVELOFF AT 6500 FT; WHICH IS ONLY ABOUT 1200 FT AGL. WE COMPLIED AND SEVERAL MI AFTER WERE TOLD TO TURN L; CLB TO 10000 FT AND CONTACT DEP. AS WE BEGAN THE TURN (SOMEWHERE AFTER DENVER VOR); OUR RADAR ALTIMETER READING SPIKED AND WE RECEIVED AUDIO 'TERRAIN; TERRAIN' WARNING. NO TERRAIN INFO CAME UP ON THE MFD. AFTER GAINING ALT I CONSULTED THE CHARTS AND SAW SEVERAL TALL TWRS ON AND AROUND THE RWY 17R CTRLINE. ONE REACHING 5759 FT WAS 5 MI S OF RWY ON THE CTRLINE AND ANOTHER; 6236 FT IS LOCATED 6 MI SSE OF THE RWY. WHETHER ANY OF THESE WERE ACTUALLY A FACTOR; AND WHETHER WE GOT ANYWHERE NEAR THEM; WE DON'T KNOW; BUT BOTH OF US WERE DISTRESSED AT BEING KEPT SO LOW IN VICINITY OF SUCH OBSTACLES. FACTORS AND THOUGHTS: THE ARPT WAS NOT BUSY; SO THERE WAS NO REASON FOR SUCH TIGHT SPACING AND RESULTANT LOW LEVELOFF. WE HAD CONSULTED THE TEXTUAL DESCRIPTION OF SINGLE ENG DEP PROC PRIOR TO TKOF; BUT I DID NOT REVIEW THE GRAPHIC; WHICH WOULD HAVE ALERTED US TO THE TWRS. WE WERE MAINLY CONCERNED ABOUT THE MOUNTAINS AND DID NOT HAVE THE TERRAIN DISPLAY UP SINCE WE WERE NOT HEADED TOWARDS THEM. I REGRET THAT. EVEN SO; WE WERE FOLLOWING ATC DIRECTIONS; AND HAD LITTLE TO NO ROOM TO MANEUVER DUE TO THE ACFT RIGHT ABOVE US. STILL; THE TERRAIN DISPLAY WOULD HAVE IMPROVED SITUATIONAL AWARENESS. I RECOMMEND CREWS CAREFULLY REVIEW SPECIAL DP CHARTS AND KEEP THE TERRAIN DISPLAY UP EVEN IN VMC.