B737 CREW RECEIVES RERTE JUST PRIOR TO PUSHBACK; AND DEPARTS SEA ON XCOUNTRY FLT WITH LESS THAN REQUIRED FUEL.

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JUST PRIOR TO PUSHBACK AT SEA; ATC ISSUED US A NEW RTE. AFTER ENTERING THE NEW RTE INTO THE FMS; ONLY ABOUT A 100 NM INCREASE IN TOTAL DISTANCE WAS NOTED. WE ALSO SENT OUR DISPATCHER THE NEW RTE VIA ACARS. THE WX WAS VFR FOR THE ENTIRE FLT. WE PUSHED BACK FROM THE GATE AND TOOK OFF 17 MINS LATER. 15 MINS INTO THE FLT; OUR DISPATCHER SENT US OUR NEW REQUIREMENTS FOR THE FLT. WE NOW NEED 3000 LBS OF EXTRA FUEL; FLYING TIME WAS 39 MINS LONGER AND TOTAL DISTANCE HAD INCREASED 233 NM AND AN ALTERNATE ARPT WAS BEING SHOWN AS BEING REQUIRED. AT THAT POINT A HIGHER CRUISE ALT WAS REQUESTED AND A LONG RANGE CRUISE SPD WAS FLOWN. WE BEGAN TO REQUEST A MORE DIRECT RTE. DURING THE NEXT 4 HRS; WE WERE ABLE TO GET FAIRLY CLOSE TO OUR ORIGINAL RTE AND LANDED WITH 2500 LBS OF FUEL ABOVE OUR MINIMUM FUEL REQUIREMENT. IF WE HAD KNOWN PRIOR TO TKOF; WE WOULD HAVE HAD MORE FUEL PUT ON BOARD. THERE MIGHT HAVE BEEN A SHIFT CHANGE WITH OUR DISPATCHER WHICH MAY HAVE BEEN THE CAUSE IN US GETTING OUR NEW NUMBERS SO LATE. I SHOULD HAVE LOOKED AT THE RTE MORE CLOSELY AND SEEN THE BIGGER DIFFERENCE BTWN THE RTES; PLUS EVERYTHING HAPPENING JUST PRIOR TO PUSHBACK ALSO HELPED CONTRIBUTE TO THE CHOICES THAT WERE MADE.