A B737 FLC FAILS TO HOLD SHORT FROM RWY 31R AS CLRED AT MDW; IL.

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CROSSED ACTIVE RWY WHEN ISSUED HOLD SHORT CLRNC. CLASSIC CASE OF MULTIPLE DISTRS CREATING A CHAIN OF EVENTS CULMINATING IN A SERIOUS SIT. BEGAN WITH TAXI IN AND LAST MIN GATE CHANGE TO UNFAMILIAR GATE. VISITING WITH TUG DRIVER; HE INFORMED ME HE WOULD PUSH BACK BTWN X AND Y TERMINAL. CLRED TO PUSH; INFORMED BY GND 'PUSH ONTO TXWY Y; TAIL TO CITY.' REPEATED CLRNC TO TUG; BUT I COULD TELL HE WAS PUSHING OFF TXWY Y. CONSIDERED TRYING TO CORRECT BUT THOUGHT TWR WAS JUST TRYING TO EXPEDITE US; AND TUG DRIVER SEEMED DETERMINED HE KNEW WHAT GND WANTED. UPON CALL FOR TAXI; GND INFORMED SHE WANTED US ON TXWY Y DUE TO ACFT PUSHING IN ALLEY. I STARTED THINKING OF MEMO ON CAPTS BEING IN COMMAND ON PUSHBACK WHEN I HEARD GND CLR TO RWY 31C VIA TXWY P; TXWY G; AND IMMEDIATELY THOUGHT 'NOT SURE BUT THINK I KNOW WHERE SHE WANTS US;' AND LOOKED AT CHART TO VERIFY. MISSED FO'S READBACK. BEGINNING TO TAXI; SAW ACFT ROLL OUT ON RWY 31R AND ASKED FO ABOUT ANY HOLD SHORT AND HE REPLIED NONE. HE WAS RETRIEVING NUMBERS BECAUSE HE HAD FAILED TO NOTE THEM BEFORE PUSH. VISUALLY CLRED RWY 31R AND TAXIED ACROSS. 2 DISTR PLTS. I BELIEVE IF HOLD CLRNC WAS ISSUED FIRST IT WOULD MAKE A DIFFERENCE. JUST HAVE TO LISTEN TO ENTIRE CLRNC.