The authors of Bicycling the Pacific Coast set out a 35 day journey from Vancouver, BC to the Mexican border, averaging about 53 miles per day. If you follow their route it is 1816.5 miles to the border (minus about 120 miles if you end your trip at LAX). You would have to average a little more than 142 miles per day for 12 days to get to LAX (151 to Mexico). Not impossible but I wouldn't want to try it.

The one thing they are insistent upon is the only way to do the route is from the north to the south. Prevailing winds make the reverse trip very difficult.