EMB135 FLT CREW HAS A RWY INCURSION ON LGA RWY 4.

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INSTRUCTION RECEIVED AND READ BACK; 'TAXI A; E; B TO 4.' AT THE INTXN OF TXWY E/B; WAS INSTRUCTED TO MONITOR TWR. WE WERE ABOUT #10 AT THIS POINT AND PROCEEDED TO MOVE UP AS ACFT WERE CLRED FOR TKOF. WHEN WE WERE NEXT TO GO; WE MOVED UP TO THE RWY HOLD SHORT LINE. AT THIS POINT THERE WA AN ACR Y ACFT ON SHORT FINAL. WE RECEIVED A CALL FROM TWR THAT W WERE 'ACROSS THE LINE OR STICKING ACROSS THE LINE AND TO TAXI ACROSS RWY 4.' WE LOOKED AT THE PROX OF THE ACFT AND THE HOLD SHORT LINE CLRLY VISIBLE IN FRONT OF US. THERE WAS DEFINITELY SOME CONFUSION; BUT TAXIING IN FRONT OF THIS CLOSE-IN LNDG TFC DID NOT SEEM LIKE THE SAFEST THING TO DO; SO I REPLIED 'NO THANKS; WE'LL WAIT UNTIL AFTER THE ACFT LANDS.' TWR INSTRUCTED THE ACR Y ACFT TO GO AROUND. WE TRIED TO GET A WORD IN ON TWR TO FIND OUT WHAT WAS GOING ON; BUT THE TWR BECAME SO BUSY THAT IT WAS BETTER TO JUST LET HIM GET TO US WHEN HE HAD A CHANCE. ANOTHER ACFT WAS SENT AROUND AND WE WERE INSTRUCTED TO TAXI ACROSS THE RWY THEN SPIN AROUND ON A COMBINATION OF TXWYS TO RWY 4. THE ATIS SAID THAT THE ILS HOLD LINE WAS BEING USED. THE ARPT DIAGRAM PAGE (10-9) SAYS THAT 'ACFT MAY BE ASKED TO HOLD SHORT OF THE ILS HOLD LINE.' FO AND I STILL BELIEVE THAT WE WERE INSTRUCTED TO TAXI TO RWY 4 VIA A; E; AND B; WHICH WE WOULD TAKE AS THE RWY HOLD SHORT LINE. GIVEN THE EXTREMELY CLR CONDITIONS AND THE TAXI INSTRUCTIONS; HOLDING SHORT OF THE ILS HOLD SHORT LINE DID NOT APPEARS TO BE THE THING TO DO.