F100 CREW HAD A RWY INCURSION AWAITING DEP AT DCA.

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XING OF HOLD SHORT LINE FOR RWY 4. WE WERE CLRED TO THE HOLDING PAD FOR RWY 4 AT DCA TO WAIT OUT A GND STOP FOR ORD. AFTER APPROX 2 HRS; WE WERE GIVEN A RERTE AND TOLD TO START ENGS AND TAXI TO HOLD SHORT OF RWY 4. I THOUGHT THE GND CTLR TOLD US TO TAXI UP TO AND HOLD SHORT OF RWY 1 (OUR DEP RWY). AS WE APCHED THE HOLD SHORT LINE FOR RWY 4; THE GND CTLR TOLD US TO HOLD OUR POS; BUT I DID NOT HEAR HIM. AS WE CROSSED THE HOLD SHORT LINE FOR RWY 4; HE AGAIN TOLD US TO HOLD POS AND THE FO FIRMLY COMMANDED ME TO STOP. WE STOPPED APPROX 20 FT PAST THE RWY 4 HOLD SHORT LINE. DCA TWR ALLOWED A COMMUTER AIRPLANE TO CONTINUE ITS APCH AND LAND ON RWY 4. WE WERE THEN TOLD TO CROSS RWY 4 AND SUBSEQUENTLY DEPARTED AND FLEW UNEVENTFULLY TO OUR DEST. THIS WAS THE LAST LEG OF A 4 LEG DAY. WE HAD BEEN ON DUTY FOR OVER 14 HRS. THIS EVENT POINTS OUT TO ME THE IMPORTANCE OF STRICTLY ADHERING TO OUR PROCS FOR HOLDING SHORT AND XING RWYS; IE; BOTH PLTS VERBALLY AGREE ON HOLD SHORT OR XING INSTRUCTIONS. PERHAPS MORE IMPORTANTLY THOUGH IT POINTS OUT HOW INSIDIOUS THE EFFECTS OF FATIGUE CAN BE. DURING THE GND STOP; WE BOTH REMARKED HOW TIRED WE WERE BECOMING. THE FO AND I BOTH AWOKE THAT DAY AT ABOUT XA15. EVEN THOUGH I KNOW WE ARE LEGAL TO REMAIN ON DUTY FOR 16 HRS; I KNOW NOW THAT FOR ME THAT MAY NOT BE A SAFE DURATION. FINALLY; WE WERE HELD AT THE HOLDING PAD FOR RWY 4; AN AREA THAT WE DO NOT NORMALLY TAXI TO. FOR A RWY 1 DEP WE NORMALLY TAXI SBOUND ON THE TAXI PARALLEL TO RWY 1 AND THEN IF NECESSARY USE THE HOLDING PAD FOR RWY 1. FO SHOULD BE COMMENDED FOR HER EXCELLENT SITUATIONAL AWARENESS AND ASSERTIVENESS. SHE ESSENTIALLY SINGLE-HANDEDLY PREVENTED A RWY INCURSION. SUPPLEMENTAL INFO FROM ACN 558141: AFTER SITTING FOR 1 HR 50 MINS; DCA GND INSTRUCTED US TO TAXI UP TO AND HOLD SHORT RWY 4. I READBACK. WE TAXIED PAST RWY 4 HOLD SHORT LINE. DCA GND SAID 'STOP.' WE STOPPED APPROX 20 FT PAST THE HOLD SHORT LINE. ACFT LANDED ON RWY 4 AND WE WERE CLRED TO CROSS RWY 4 AND HOLD SHORT RWY 1 AND MONITOR TWR. WE DEPARTED INCIDENT FREE. THIS COULD HAVE BEEN AVOIDED IF I HAD VERIFIED THE HOLD SHORT WITH THE CAPT. I WAS OPERATING ON AN EARLY WAKE-UP TIME. THIS EVENT MADE ME REALIZE THAT MY PERSONAL DUTY DAY LIMIT IS 14 HRS.