B737-800 FLC BECAME STRANDED ON TXWY DURING TAXI OUT DUE TO SINKING INTO ASPHALT TXWY AFTER HOLDING FOR TKOF.

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OUR ACFT WEIGHED APPROX 154200 LBS AT PUSHBACK. SKY WAS SUNNY. ENG MANIFOLD PRESSURE 35 DEGS C (USING ONBOARD SAT READING). AFTER STOPPING IN LINE-UP AT POINT DESCRIBED ABOVE; ACFT WOULD NOT MOVE USING MORE THAN NORMAL TAXI PWR. ACFT BEHIND COMPLAINED OF JET BLAST; GND CREATED CLR SPACE. ACFT STILL WOULDN'T MOVE USING WELL ABOVE NORMAL TAXI PWR (2 ENGS). 40% N1 IS NORMAL; WE TRIED 68% N1. CALLED FOR TUG; TOW BAR SHEAR PIN BRAKE. DEPLANED PAX; BROKE ANOTHER TOW BAR. RESTARTED ENGS WITH ONLY FLC ONBOARD (PLTS AND FLT ATTENDANTS) AND WITH ACFT WT NOW APPROX 30000 LBS LESS; WE BROKE FREE AT +/-75% N1. WE TAXIED TO KNOWN SOLID SPOT ON RAMP. MECH AND I INSPECTED ACFT GEAR AND TIRES; REBOARDED FLT; TAXIED FOR TKOF AND FLEW TO DEST. LESSONS LEARNED: LGA HAS SOFT SPOTS ON TXWYS ON HOT DAYS. (WE SANK 6 INCHES INTO TXWY.) B737-800 HAS HVY FOOTPRINT (MY GUESSTIMATE HAD US NEAR 2000 PSI). NYC PORT AUTH WAS RESPONSIVE AND HELPFUL (VERY). SAME FOR LGA GND CTL AND MY COMPANY'S LCL RAMP PERSONNEL. B737-800 TOW BAR SHEAR PIN SHEARS EASILY (TOO EASILY?). IDEAS TO PREVENT RECURRENCE: WITH CORRECT TECHNICAL DATA; CERTAIN ACFT TYPES IDENTED AS HVY FOOTPRINT TYPES COULD; ON HOT DAYS: 1) BE HELD AT GATE UNTIL EXPEDITIOUS TAXI TO TKOF OR KNOWN SOLID HOLDING AREA IS POSSIBLE (MUCH LIKE LGA'S DE-/ANTI-ICING PROGRAM). 2) BE ROUTED OVER KNOWN SOLID TXWYS. 3) RE-PAVE LGA'S TXWYS WITH CONCRETE. THE COST OF ANY PROGRAM TO PREVENT ACFT GETTING STUCK IN LGA'S ASPHALT WOULD HAVE TO BE WEIGHED AGAINST THE THREAT OF SUCH RECURRENCE. I DON'T THINK WHAT HAPPENED TO US IS AN EVERYDAY EVENT. THAT'S A GOOD THING -- BECAUSE IT WASN'T FUN!