TKOF ABORTED. OTHER ACR IN RWY INCURSION.

Narrative

LGA TWR WAS IN THE MIDDLE OF CHANGING LNDG RWY TO THE SAME RWY AS TKOF (RWY 4; BRAKING ACTION POOR TO NIL; RWY 13). WE HAD ALREADY PASSED HOLD SHORT LINE #2 FOR HOLD SHORT LINE #1; WHEN TWR TOLD US TO HOLD SHORT OF HOLD LINE #2. WE TOLD THEM WE PASSED IT ALREADY (THE ATIS WE HAD SAID 'HOLD SHORT LINE #1 WAS IN USE'). SINCE WE PASSED LINE #2; APPARENTLY THEY WANTED TO GET US OUT BEFORE THE FIRST ILS RWY 4 ARR BECAUSE WE WERE IN THE ILS CRITICAL AREA. WE WERE GIVEN 'POS AND HOLD RWY 4.' WHILE IN POS; I NOTICED 2 JETS TAXI ACROSS OUR RWY. WE WERE THEN 'CLRED FOR TKOF; SOME JET 2 MI FINAL RWY 4.' AT ABOUT 70 KIAS ACR Y'S AIRBUS CAME INTO VIEW TAXIING ACROSS OUR RWY (LOOKING AT THE ARPT DIAGRAM; THEY WERE TAXIING R TO L ON TXWY 'F'). I CALLED 'ABORT; ABORT' AND THE FO (PF) ABORTED THE TKOF. WE CAME TO A FULL STOP ABEAM TXWY 'D.' DURING THE ABORT I ANNOUNCED ON TWR FREQ THAT; 'ACR X IS ABORTING OUR TKOF; AN ACR Y AIRBUS IS TAXIING ACROSS THE RWY. 'THERE WAS NO IMMEDIATE RESPONSE FROM TWR. A FEW SECONDS LATER; THE JET ON FINAL ASKED; 'IS THE RWY CLR YET?' WE WERE IN OUR TURN; CLRING THE RWY; WHEN TWR IMMEDIATELY INSTRUCTED THE JET ON FINAL TO 'GAR.' IF THE VISIBILITY WAS MUCH LOWER; WE MAY NOT HAVE BEEN ABLE TO STOP (I.E.; HIGHER SPD AND LESS DISTANCE TO STOP); AND WITH POSSIBLY NO RADIO CALL FROM EITHER (POTENTIALLY CRASHED) ACFT ON THE GND; THE LNDG ACFT COULD HAVE JOINED THE PILE-UP WITH NO WARNING. SINCE WE HAD PASSED INTO THE ILS CRITICAL AREA; TWR MAY HAVE BEEN PRESSURED TO GET US OUT QUICKLY TO AVOID MAKING THE ACFT ON FINAL 'GO MISSED.' I DON'T KNOW WHY ACR Y WAS ON OUR RWY. EITHER GND TOLD THEM TO CROSS AND DIDN'T COORDINATE WITH TWR; OR ACR Y WAS SLOWER THAN THEY EXPECTED XING; OR ACR Y WAS DISORIENTED AND CROSSED UNKNOWINGLY. LOW VISIBILITY WAS DEFINITELY A FACTOR.