A B737-500 CREW; ARRIVING GEG; DECLARED A 'MINIMUM FUEL' SIT DUE TO RWY CLOSURE AND EXCESSIVE HOLDING.

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OUR DIVERT AND MINIMUM FUEL SIT STARTED WITH A RWY CLOSURE AT GEG. AS WE ENTERED DOWNWIND FOR THE ILS TO RWY 21 GEG; AN EMER ACFT LANDED ON AND CLOSED THE RWY. INITIALLY; NOT KNOWING HOW LONG IT WOULD BE CLOSED WE ENTERED HOLDING AT PHORT. AFTER 1 TURN IN HOLDING WITH SUFFICIENT WX; WE EXECUTED THE ILS IN ORDER TO CIRCLE TO LAND RWY 25. WE DID NOT HAVE ENOUGH VISUAL CUES AND EXECUTED A GAR AT THE MISSED APCH. AT THIS POINT; A COMMUTER ACFT ATTEMPTED AN OPPOSITE DIRECTION APCH AND WE GOT VECTORS W OF THE FIELD; WAITING TO SEE IF HE WAS SUCCESSFUL. AT THIS POINT; WE GOT DISPATCH INVOLVED AND CALCULATED A DIVERT FUEL FOR BOI. THE OPPOSITE DIRECTION APCH WAS UNSUCCESSFUL AND APCH CTL EXTENDED THE CLOSURE TIME TO 30-40 MORE MINS. AT THIS POINT; WE BEGAN OUR DIVERT TO BOI; THEN GOT REDIRECTED TO SEA BY DISPATCH. THE INITIAL FMC FUELS SHOWED ARR AT SEA WITH JUST OVER 4000 LBS; BUT A SLIGHT DELAY AT A LOWER THAN EXPECTED ALT FOR TFC DROPPED OUR ARR FUEL TO 3900 LBS. PER FOM DIRECTION WE WERE MINIMUM FUEL AND DECLARED IT AT THAT POINT. WITH NO OTHER DELAYS; WE LANDED AT SEA WITH 4000 LBS OF FUEL.