B757 FLT CREW ELECTS TO ACCEPT AN UNSTABILIZED APCH INTO MDW AND IS UNABLE TO STOP THE ACFT ON THE RWY COLLIDING WITH A BLAST FENCE AT THE END.

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THE LAST AVAILABLE ATIS RPTED WINDS 140 DEGS AT 8 KTS; VISIBILITY 10 SM WITH FEW CLOUDS AT 11000 FT WITH HIGHER SCATTERED AND BROKEN LAYERS. WE WERE BEING VECTORED FROM BTWN BVT AND CGT ON THE BVT2 ARR AT 6000 FT FOR THE ILS RWY 31C AND WERE GIVEN A VECTOR TO JOIN THE LOC WITH A DSCNT TO 4000 FT. THE ACFT WAS BEING FLOWN ON AUTOPLT AT 250 KTS. I NOTICED THAT THE VECTOR TOOK US JUST INSIDE GLEAM; ONE OF THE STEP DOWN FIXES ON THE APCH. I ASKED FOR THE FO TO GIVE ME AN INTERCEPT LEG TO GLEAM AND WIDENED OUT THE APCH SLIGHTLY BY SELECTING DIRECT GLEAM AND LNAV. UPON REACHING GLEAM; WE WERE CLRED FOR THE APCH. I SELECTED APCH MODE ON THE MCP. THE LOC CAPTURED IMMEDIATELY; BUT THE GS ONLY ARMED WITHOUT CAPTURE. WE WERE SHOWING JUST A FRACTION HIGH ON THE GS. ALTHOUGH I WAS ANXIOUS TO START A SPD REDUCTION; I SELECTED FLT LEVEL CHANGE AND KEPT THE SPD UP JUST LONG ENOUGH TO GET GS CAPTURE. AT THIS POINT; I BEGAN BUGGING THE SPD BACK AND SEQUENTIALLY SELECTING FLAPS AT THE APPROPRIATE MANEUVERING SPD. THE ACFT WAS DECELERATING MORE SLOWLY THAN IS NORMAL. I DEPLOYED THE SPD BRAKE PRIOR TO GS CAPTURE; AND BELIEVE I CALLED FOR GEAR DOWN SHORTLY AFTER FLAPS 1. SPD WAS STILL EXCESSIVE. AT THIS POINT; A MISSED APCH WOULD HAVE BEEN AN EXCELLENT IDEA. THE FO CALLED OUT SEVERAL TIMES 'ARE WE GOING TO MAKE IT?' ALTHOUGH THIS IS NOT A STANDARD CALL; HIS MEANING WAS CLR ENOUGH; AND THIS SHOULD HAVE PROMPTED ME TO EXECUTE A MISS. THE ACFT FLOATED A LONG WAYS BEFORE FINALLY TOUCHING DOWN. I WAS UNABLE TO STOP ON THE RWY EVEN WITH HARD BRAKING AND REVERSE THRUST. THE NOSE OF THE ACFT PENETRATED THE FRANGIBLE BLAST FENCE AND THE ACFT CAME TO REST WITH THE NOSE 20 FT OFF THE RWY. LEVELS OF IMPACT TO THE ACFT SEEMED MINIMAL. I ELECTED NOT TO ORDER AN EMER EVAC. WE DID START THE APU AND SHUT THE ENGS DOWN. ARRANGEMENTS WERE MADE TO OFFLOAD THE PAX WITH MOBILE STAIRS. AFTER CALLING PLT SUPVR ON A CELL PHONE WE PULLED THE CIRCUIT BREAKER AT HIS REQUEST. THE CABIN CREW RPTED THAT NO ONE APPEARED INJURED; AND THEY ALONG WITH RAMP AND EMER CREWS; PERFORMED THEIR DUTIES QUICKLY AND EFFICIENTLY. SUPPLEMENTAL INFO FROM ACN 593094: HE WAS KEEPING THE SPD UP MORE THAN I WAS COMFORTABLE WITH; AND I VOICED MY CONCERN TO HIM. WE CONFIGURED FOR THE LNDG; AND THE PF BEYOND MY NUMEROUS QUESTIONS ABOUT THE APCH -- CONTINUED. WE CROSSED THE THRESHOLD FAST AND TOUCHED DOWN LONG. I CONTINUED MY VERBAL QUESTION ALL THE WAY INTO THE FLARE AS FAST AS I COULD GET THE WORDS OUT OF MY MOUTH -- BUT WE WERE TOUCHING DOWN. FACTORS WERE -- SENIOR CAPT (PF) -- PAIRED UP WITH NEW FO; A TAILWIND ON FINAL; AND FAILURE TO REJECT THE APCH AND LNDG.