A B737-300 DURING PUSHBACK OP WAS PUSHED INTO PROX OF A TAXIING B737 NARROWLY AVOIDING A COLLISION. CAUSED BY PUSHBACK CREW LACK OF VIGILANCE.

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WE WERE PARKED AT THE GATE. GND CLRED US TO PUSH. FO TOLD ME 'CLRED TO PUSH.' I CLRED THE PUSH CREW TO PROCEED AND CALLED FOR 'START #2.' FO RESPONDED WITH 'START #2.' SINCE WE WERE TAKING OFF ON RWY 31L AND IT WOULD BE A SHORT TAXI; THE FO SECURED THE DOOR AND THE JUMP SEAT AS THERE #2 ENG SPUN UP. I HEARD GARBLED RADIO XMISSIONS ON BOTH COM #1 AND COM #2. AFTER WE CLRED THE JETWAY BY 20 FT AND BEGAN TO START #1; I SAW A JET TO MY L; ON THE TAXI OUT YELLOW LINE POINTED AT ME. I INSTRUCTED THE PUSH CREW TO PUSH US BACK FAR ENOUGH TO GIVE THAT JET TAXI SPACE. POST START; TAXI; TKOF WERE NORMAL. ON CLBOUT; PAST 1000 FT; ACR Y ABCD CALLED US AND TOLD US OF THE NEAR MISS ON PUSHBACK. THEY TOLD US THE WINGWALKER WATCHED EVERYTHING; BUT DID NOTHING. THEY ALSO TOLD US THEY CALLED ON THE RADIO; I DON'T KNOW WHICH ONE AND DIDN'T HEAR ANY 'STOP THE PUSH' RADIO CALLS. OBVIOUSLY; THE GARBLED RADIO XMISSIONS I HEARD CONTAINED THE STOP PUSH CALL; BUT IT DIDN'T ALERT ME TO POTENTIAL TROUBLE. I TOLD ABC I WOULD CALL ZZZZ. ENRTE TO MHT MY FO AND I DISCUSSED THE EVENTS; WE DECIDED TO WAIT UNTIL THE PUSH WAS COMPLETE TO SECURE THE DOOR/JUMP SEAT. SINCE I ALWAYS LISTEN TO BOTH COM #1 AND #2; I WILL TRY TO REACT MORE ACTIVELY TO GARBLED RADIO XMISSIONS. SINCE GND DIDN'T GIVE MY FO ANY TFC IMPACT ON OUR PUSH; I WAS VERY SURPRISED AT OUR CONFLICT WITH ABCD. IN MHT; I CALLED ZZZZ AND SPOKE WITH THE GATE RAMP SUPVR. I EXPLAINED THE EVENT AND HE WAS VERY CONCERNED ABOUT PUSH CREW VIGILANCE. HE SAID HE WOULD SPEAK WITH THE GATE SUPVR AND THE PUSH CREW.