A320 FLT WAS DELAYED AND DEPARTED OVER 5 HOURS LATE. FLT CREW WAS SUFFICIENTLY FATIGUED THAT AN ENROUTE NAP WAS NECESSARY DURING CRUISE.

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EXPERIENCED FATIGUE FOLLOWING AN ALL-NIGHTER AND EXTENDED NEXT DAY DEP DELAY. WE FLEW AN ALL-NIGHT FLT FROM ZZZ-EWR AND ARRIVED AT ABOUT XA00 LCL AND WENT TO BED AT ABOUT XB00 LCL. WHILE AT THE HOTEL; SHERATON ARPT; WE WERE AWAKEN TO SOUND OF THE FIRE EMER EVAC AT AROUND XC00; JUST AS I HAD FALLEN ASLEEP. THE FIRE WARNING LASTED ABOUT 10 MINS; IT WAS ANNOYINGLY EFFECTIVE AND DISRUPTED MY SLEEP PATTERN MAKING IT DIFFICULT TO FALL ASLEEP EASILY AGAIN. AFTER A FEW HRS OF POOR SLEEP; AS IS TYPICAL WITH ALL-NIGHTERS; I GOT UP. I MET THE FO IN THE LOBBY AND WENT TO THE ARPT FOR OUR ASSIGNED FLT TO ZZZ1. OUR AIRPLANE HAD NOT ARRIVED AND THUS WE HAD TO WAIT IN THE TERMINAL. OUR SCHEDULE DEP WAS FOR XL00 LCL; BUT WE BLOCKED OUT 57 MINS LATE DUE TO CONVECTIVE WX IN THE AREA AND IN THE CENTRAL UNITED STATES. AS WE APCHED THE DEP RWY 22R; ATC ADVISED THAT THE DEPS WERE CLOSED. OVER THE NEXT 3 HRS WHILE OUT NEAR THE RWY WE WERE GIVEN 5-6 FULL REROUTES; EACH INVOLVING RE-ENTRIES INTO THE FMGC AND COORD WITH DISPATCH. REALIZING THAT THE FLT WAS NOT GOING TO DEPART FOR ANOTHER 2 OR MORE HRS I ELECTED TO GO BACK TO THE GATE TO ALLOW THE PAX A CHANCE STRETCH; GET FOOD; ETC. ONCE AT THE GATE I BEGAN TO THINK OF WHEN AND IF WE WOULD GET OUT; COORDINATION WITH DISPATCH; THE CREW DESK; CUSTOMER SVC; EXPLAINING TO THE PAX; ETC. A LINE OF TSTMS WAS ABOUT TO PASS OVER THE ARPT AND ATC SAID THE ARPT WOULD BE SHUT DOWN FOR SEVERAL HRS. IT WAS ABOUT XP00 LCL; WHEN I REALIZED THAT WE SHOULD BE LNDG IN ABOUT 1 HR; HAD WE LEFT ON TIME; AND AT THIS RATE WE WOULD BE LNDG WELL AFTER XT00 CREW BODY TIME; FATIGUE WOULD NOW BE A CONCERN AT THE ARR PORTION OF THE FLT. I TOLD THE FO; THE FLT ATTENDANTS; THE PAX AND THE COMPANY THAT I DID NOT THINK IT WAS PRUDENT FOR US TO DEPART IF IT WENT BEYOND XQ00-XR00 LCL DUE TO MY CONCERN FOR FATIGUE. THE PAX; FLT ATTENDANTS; CREW DESK; DISPATCH WERE ACCEPTING OF MY DECISION AND CONCERN; HOWEVER SOME AT THE DISPATCH STATION WERE RATHER BOTHERED AND UNSUPPORTIVE THAT I WOULD NOT TAKE THE FLT OUT; NO MATTER WHEN WE WENT! I TRIED TO EXPLAIN IN A PROFESSIONAL AND RESPECTFUL MANNER THAT WE HAD ARRIVED FROM AN ALL-NIGHTER THAT MORNING AND THAT MY BODY COULD NOT FUNCTION SAFELY BEYOND A CERTAIN TIME. I GOT A SMART REMARK FROM 1 FEMALE AGENT SAYING HOW SHE WAS TIRED RATHER THAN BEING SUPPORTIVE AND RESPECTFUL OF MY DECISION. IN ANY CASE WE WANTED TO HELP THE PAX GET OUT OF EWR AS THERE WERE NO LCL HOTEL ROOMS AVAILABLE IF WE CANCELED. DISPATCH WAS QUICK TO GET US A RTE TO EXPEDITE OUR DEP AND SO WE DEPARTED QUICKLY AROUND XQ30 PM. ENRTE PAST ALL THE WX; APCHING DEN; AND NOW IN VMC; FATIGUE QUICKLY BEGAN TO TAKE HOLD. WE TURNED THE COCKPIT LIGHTS UP BRIGHT; TALKED; BUT STILL FELT EXHAUSTED. I COULD NO LONGER STAY AWAY AND ALERT; SO I TOLD THE FO THAT I NEEDED TO CLOSE MY EYES FOR 15 MINS AND I SET MY ALARM FOR 15 MINS AND RESTED. AFTER THE REST I FELT MUCH BETTER AND CAPABLE OF THINKING AND MAKING DECISIONS WITH BETTER CLARITY. I THEN TOLD THE FO IF HE NEEDED A SHORT BREAK TO TAKE ONE; HE SAID HE DIDN'T. ABOUT 1 HR OUT FROM LNDG I BEGAN TO NOTICE THE FO NODDING OFF INVOLUNTARILY. I TURNED TO HIM AND TOLD HIM THAT HE WAS FALLING ASLEEP AND THAT I URGE HIM TO CLOSE HIS EYES FOR 15 MINS; THE WX WAS CLR; I FELT FINE AND THAT IT WOULD BE PRUDENT TO DO SO. HE RESTED AND ONCE AWAKE HE FUNCTIONED MORE ALERTLY. WE MADE A DSCNT AND ARR INTO ZZZ; SAFELY AND ALERT!