B737 CAPT STOPPED SHORT OF RWY; BUT PAST HOLD SHORT LINE FOR A SMA ON A SHORT FINAL EVEN THOUGH TWR HAD CLRED HIM TO CROSS THE RWY DURING TAXI TO PARKING. TWR CTLR SENT SMA AROUND AFTER BEING INFORMED OF RPTR HOLDING SHORT.

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AFTER LNDG ON CID RWY 27 AND EXITING THE RWY AT TXWY B1; CID TWR; GND CTLR CLRED US TO 'TAXI TO THE RAMP' VIA TXWY B. APCHING THE TXWY B; RWY 31 INTXN; SINCE WE HEARD TWR GND CONVERSING WITH LNDG LIGHT ACFT TFC; I ASKED MY COPLT TO VERIFY; CONFIRM OUR CLRNC TO CROSS RWY 31. JUST THEN; AND BEFORE WE COULD ASK; TWR GND CALLED US SPECIFICALLY; CLRING US TO CROSS RWY 31 AND ADVISED US OF TFC (A CESSNA OR CHEROKEE; I THINK) ON THE APCH TO RWY 31. GND THEN CLRED THE GA TO LAND AND ADVISED HIM OF THE TFC XING RWY 31 ON TXWY B (US). WHILE TAXIING EXPEDITIOUSLY TOWARD THE TXWY B; RWY 31 INTXN; THE NEXT EVENTS HAPPENED ALMOST SIMULTANEOUSLY. I SAW AND CALLED OUT A GA TURNING TOWARD LNDG ON RWY 31 JUST AS WE WERE XING THE TXWY B1 RWY 31 INTXN HOLD SHORT LINE. THE JUMPSEATING FO CALLED OUT THAT THE GA WAS LNDG. WE (CAPT; COPLT AND JUMPSEATER) ALL FELT THE GA WAS TOO CLOSE TO LNDG FOR US TO CROSS SAFELY. I DECIDED THAT RATHER THAN PUSH A POTENTIALLY BAD SITUATION; IT WAS BEST TO BREAK THE SAFETY CHAIN AND STOP; EVEN THOUGH WE WERE ACROSS THE HOLD SHORT LINE (BUT SHORT OF THE RWY). COPLT NOTIFIED GND THAT WE HAD STOPPED SHORT OF RWY BUT ACROSS THE HOLD SHORT LINE. GA EXECUTED A GAR. WE THEN RECEIVED CLRNC TO CONTINUE OUR TAXI ACROSS THE RWY TO THE RAMP; AND TAXIED TO PARKING UNEVENTFULLY.