A B737-300 CREW AND A C152 OR C172 HAD AN NMAC IN GEG CLASS C AIRSPACE. THE ATCT LCL CTLR GAVE A LATE TA AND DID NOT GIVE CLRNCS TO SEPARATE THE ACFT.

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FLT WAS TO SPOKANE. WX WAS GOOD AND NOT A FACTOR. FLT WAS UNEVENTFUL UNTIL ON FINAL APCH TO RWY 21 AT GEG. WE APCHED GEG FROM THE S; ANTICIPATING A VISUAL APCH TO RWY 21. ON L BASE; APCH CTL CALLED OUT TFC AHEAD AND TO OUR L. THE TFC WAS A KC-135 ON APCH TO FAIRCHILD AFB. WE CALLED THE TFC IN SIGHT AND WERE THEN CLRED FOR A VISUAL APCH TO RWY 21. AS WE STARTED A TURN TO FINAL; WE WERE TOLD TO CONTACT TWR. AFTER CHK-IN WITH TWR; WE WERE CLRED TO LAND ON RWY 21. VERY SHORTLY AFTER; TWR CALLED OUT TFC CLOSE-IN AND TO OUR L. WITHIN SECONDS OF THIS TFC CALL BY TWR; WE RECEIVED A TCASII RA TO CLB. AT THIS TIME; WE WERE ON APPROX 5 MI FINAL AT 1500 FT AGL. WHILE EXECUTING THE RA AVOIDANCE MANEUVER; WE VISUALLY ACQUIRED THE TFC AS WE PASSED DIRECTLY OVER IT. WE ESTIMATE WE PASSED 400 FT ABOVE THE TFC. TFC APPEARED TO BE A C152 OR C172. AFTER THE NMAC; WE ASKED TWR FOR A 360 DEG TURN TO REPOS FOR A NORMAL APCH. WE SUBSEQUENTLY LANDED WITHOUT INCIDENT. AFTER SHUTDOWN AT THE GATE; I EXPLAINED TO THE PAX WHAT HAD HAPPENED. SUPPLEMENTAL INFO FROM ACN 592914: SUDDENLY; POP-UP TFC ON FINAL STRAIGHT AHEAD CAUSED OUR TCASII TO SOUND OFF AN RA TO CLB. WE VISUALLY ACQUIRED A CESSNA; SE XING FINAL GOING NW; AT OUR ALT. IF THE CAPT HADN'T COMPLIED WITH THE RA TO CLB GIVEN BY TCASII; I BELIEVE A MIDAIR COLLISION WOULD HAVE BEEN THE OUTCOME. WE WERE SO BUSY LOOKING OUTSIDE THAT I MISSED THE ACTUAL NUMBER OF FT THAT WE CLRED THE SE ACFT. I BELIEVE IT WAS ABOUT 300-400 FT.