FO OF A B727 ABRUPTLY STOPPED THE ACFT DURING TAXI WHEN HE NOTICED A BEECHCRAFT KING AIR ROLLING OUT ON THE RWY PREVIOUSLY CLRED TO CROSS BY TWR.

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WE HAD TAXIED TO THE HOLD SHORT AREA FOR RWY 18 FOR DEP AND HAD SHUT DOWN OUR ENGS DUE TO DELAYS DUE TO WX ENRTE. AFTER ABOUT AN HR DELAY; WE WERE INSTRUCTED BY DCA TWR TO START OUR ENGS AND RPT WHEN READY FOR TAXI. WHEN WE CALLED FOR TAXI; TWR ADVISED US THAT THEY WERE NOW USING RWY 36 DUE TO WIND SHIFT AND WE WERE TO FOLLOW AN ACR Z B737 TO RWY 36 VIA TXWY J; THE PARALLEL. THIS REQUIRED US TO CROSS RWY 15 SHORTLY AFTER WE PULLED OUT OF THE HOLD SHORT AREA FOR RWY 18. WHEN THE TWR INSTRUCTED US TO TAXI TO RWY 36 AND FOLLOW THE ACR Z B737 THEY SPECIFICALLY TOLD US TO 'CROSS RWY 15.' THE COPLT READ BACK THE CLRNC EXACTLY AS THE TWR GAVE IT. ABOUT 30 SECONDS AFTER THE TWR'S INITIAL CLRNC; THE TWR REPEATED ITS INITIAL CALL. THE COPLT REPEATED THE READBACK TO CROSS RWY 15. I WASN'T SURE WHY THE TWR FELT IT HAD TO REPEAT ITS INSTRUCTIONS TO US BECAUSE WE WERE RESPONDING TO THE FIRST CALL AND OUR COPLT HAD ANSWERED IT. AS WE APCHED RWY 15; I FELT THE ACFT COME TO AN ABRUPT STOP AS THE COPLT YELLED 'STOP!' TO THE CAPT. SHORTLY THEREAFTER; I SAW A KING AIR PASS IN FRONT OF US AS IT WAS APPARENTLY ROLLING OUT ON RWY 15. AS WE WERE STOPPING; THE TWR SAID 'ACR X STOP!' XMISSIONS FROM THE TWR TO US AND OTHER ACFT FROM THE TIME WE WERE TOLD TO START ENGS UNTIL THIS INCIDENT WERE CLR AND COMPLETE. WE HEARD NO XMISSIONS THAT CAUSED US TO DOUBT WHETHER WE HAD CLRNC TO CROSS RWY 15; WHICH HAD BEEN IN USE IN ADDITION TO RWY 18. THERE WERE NO BLOCKED XMISSIONS. HAD THE COPLT NOT BEEN CLRING OUR XING OF RWY 15; WE WOULD PROBABLY HAD BEEN HIT BY THE KING AIR. SINCE WE WERE ANGLING AWAY FROM THE APCH END OF RWY 15; IT WAS DIFFICULT FOR THE CAPT AND IMPOSSIBLE FOR ME (THE SO) TO SEE TFC ON RWY 15 COMING FROM OUR 4-5 O'CLOCK POS. AFTER THE KING AIR PASSED; TWR INSTRUCTED US TO CROSS RWY 15 AND TO CONTINUE TAXIING TO RWY 36. ONCE WE CROSSED RWY 15; WE WERE TOLD TO SWITCH TO GND CTL. THE TWR MADE NO COMMENTS ABOUT THE POTENTIAL COLLISION TO US OR THE KING AIR. I DON'T KNOW IF THE KING AIR LANDED ON THE WRONG RWY OR IF THE TWR CTLR LOST TRACK OF THE KING AIR IN THE PROCESS OF TURNING THE AIRFIELD AROUND. THE COPLT IN THIS SIT WAS A SEASONED B727 COPLT WHO TOOK HIS RESPONSIBILITIES SERIOUSLY AND WHO; FORTUNATELY; WAS DOING HIS JOB OF CLRING THE RWY WE WERE ABOUT TO CROSS. HE RESPONDED INSTINCTIVELY AND APPLIED THE BRAKES SIMULTANEOUSLY AS HE YELLED TO THE CAPT TO 'STOP!' HAD HE HESITATED; OR NOT BEEN PAYING ATTN; THE KING AIR PROBABLY WOULD HAVE HIT US. I'M SURE THE FACT THAT THE CAPT PRACTICED GOOD CRM TECHNIQUES AND MADE US ALL FEEL PART OF THE TEAM CONTRIBUTED TO THE COPLT'S RESPONSE. THE TWR WAS IN THE BEST POS AND HAD THE RESPONSIBILITY TO AVERT THIS SIT. WE WERE (THE COPLT THAT IS) THE LAST LINK IN THE CHAIN. WE WERE ALREADY BRAKING TO A STOP WHEN THE TWR YELLED 'ACR X; STOP!' THE FEW SECONDS THE COPLT GAVE US PROBABLY AVERTED A COLLISION AND MADE ALL THE DIFFERENCE IN THE WORLD.