I believe it's 100 pounds a day with a saltwater fishing license. I don't think FWS monitors public beaches for this much. I prefer to dip net algae in the surf so there are more inverts, just watch out for swimmer and decorator crabs.
Also, bay and lagoon inlets are natural funnels for algae washed in by tides. Use google earth to find even small inlets near where you are staying. Just beware of huge differences in salinity. This time of year, low rainfall drives salinity north of 1.029 where I collect near Cocoa.