A B737-300 TAXIES PAST THE HOLD SHORT LINE OF RWY 31R AT MDW AFTER BEING TOLD TO FOLLOW SECOND COMPANY ACFT TO RWY 31C; MDW; IL.

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FLT PUSHED FROM GATE. GND WAS VERY BUSY WITH NUMEROUS ACFT REQUESTING MOVEMENT. AFTER PUSH; GND ASKED IF WE WERE READY FOR TAXI (TO CLR THE ALLEY) AND I RESPONDED THAT WE WERE. THERE WAS NO RESPONSE; SO A MOMENT LATER I REQUESTED TAXI. A PREVIOUS ACFT HAD BEEN TOLD TO HOLD SHORT WHICH MADE ME ALERT TO THAT POSSIBILITY. (HOLD SHORT OF RWY 31R ENRTE TO RWY 31C.) TO THE BEST OF MY RECOLLECTION GND TOLD US TO TAXI AFTER THE SECOND PASSING ACFT (PASSING R TO L ON TXWY E) TO RWY 31C. I RESPONDED 'BEHIND THE SECOND ACFT TO RWY 31C.' AS WE APCHED RWY 31R; THE CAPT ASKED IF WE WERE CLRED TO RWY 31C AND I CONFIRMED WE WERE TO HIM (BUT NOT WITH GND). WHEN WE CROSSED THE HOLD SHORT LINE; GND TOLD US WE WERE NOT CLRED ACROSS. THEY TOLD US TO EXPEDITE ACROSS; AND TO MAINTAIN SAFE CLRNC; SENT A COMMUTER AROUND (FROM ABOUT 2 NM FINAL). ANALYSIS: GND WAS VERY BUSY. THEY EITHER CONFUSED WHAT THEY TOLD US TO DO; OR I SOMEHOW MISSED THE CLRNC. IN EITHER CASE; I DID NOT ACKNOWLEDGE THE HOLD SHORT INSTRUCTIONS. FIX: KNOWING THINGS WERE VERY BUSY; WE SHOULD HAVE BEEN GEARED TO MORE PRECAUTION. WHEN THE CAPT EXPRESSED THE SLIGHTEST DOUBT ABOUT THE CLRNC; I SHOULD HAVE CONFIRMED IT WITH GND BEFORE PENETRATING RWY 31R. P.S. WE TALKED WITH THE MDW SUPVR. HE SAID NO SAFE DISTANCES WERE PENETRATED. HE HAD NOT REVIEWED TAPES AT THAT TIME. SUPPLEMENTAL INFO FROM ACN 459672: THEY REPLIED THAT WE WERE NOT CLRED TO CROSS RWY 31R AND THAT WE WERE TOLD TO HOLD SHORT OF RWY 31R.