A319 FLT CREW WAS FORCED TO APPLY HEAVY BRAKING TO AVOID ACFT MAKING A LOW APCH.

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WE PUSHED BACK FROM THE GATE; STARTED BOTH ENGS AND EXTENDED THE FLAPS AND COMPLETED THE SAFETY CHKS. WE NOTIFIED GND THAT WE WERE READY TO TAXI. WE WERE TOLD TO HOLD SHORT OF THE TXWY L LINE AND CONTACT TWR. WE PULLED UP TO TXWY L AND HELD SHORT OF THE INTXN 90 DEGS TO THE RWY. WE THEN CONTACTED THE TWR. THE FO REPEATED THE CLRNC. THE TWR CLRED US TO CROSS RWY 16R TO HOLD SHORT OF RWY 16L. I TURNED THE CORNER TO CROSS THE RWY. PRIOR TO XING THE RWY MARKINGS I LOOKED TO THE L TO MAKE SURE THE FINAL WAS CLR. I WAS SURPRISED TO SEE A SINGLE ENG CESSNA MAKING A DIVING APCH TO THE RWY. I SLAMMED ON THE BRAKES AND HELD SHORT OF THE RWY. WE DID NOT CROSS THE RWY THRESHOLD MARKINGS. THE ACFT MADE A LOW APCH AND CONTINUED ON. AS THE CESSNA WAS ABEAM US THE TWR ONCE AGAIN CLRED US TO CROSS THE RWY. THE ACFT'S LOW APCH WAS LOW ENOUGH THAT HAD WE CROSSED THE RWY; I AM SURE HE WOULD HAVE HIT OUR TAIL. AT NO TIME DID THE TWR MENTION THE ACFT MAKING THE LOW APCH TO US. WE DID NOT CROSS ANY RWY THRESHOLD UNTIL AFTER THE SECOND CLRNC AND THE ACFT HAD PASSED US.