You just don't get it. DC-10s and L-1011s have the performance to do the job that they did flying out of LGA (as did the A300s and B767s that have also served LGA.) But they NEVER flew them to the west coast, either.
The size of the airplane has nothing at all to do with its performance and range. If the taxiways and runways were stressed for the weight, one could fly C-5s, B-747s and A-380s out of LGA. They just could not go as far as they are designed to go.
So, then....believe it. 737-800s can't fly off the relatively short LGA runways AND GO ALL THE WAY TO THE WEST COAST.
And, I bet the DC-10 and L1011 couldn't, either, with a full load of passengers and luggage.
(I came back to add another point)
I think folks are under the impression that airliners land and fill up their fuel tanks and go. That almost never happens. The amount of fuel is carefully calculated based on stage length, anticipated delays, winds aloft and many other factors. When it (rarely) happens that an airplane needs to fill its tanks to meet those requirements for a particular flight, then there are usually restrictions on passenger loads (blocked seats) and cargo. If the takeoff runway is also short, then even more restrictions are placed. The 737-800 might be able to go to LAX out of LGA (I don't fly it, so I don't really know for sure...and I have no real reason to research it because the principle is the same for all airplanes). But if one loaded enough fuel and given the runway length, it would probably have so many seats blocked that it would never be profitable.
The B757 is probably the only airliner flying that can actually fill its tank (and thereby have the necessary range for transcon) and still carry a respectable load of passengers and cargo. Some say the 737-700 can do it, but I can't verify that since I have never operated one.