Here's am idea of how many members it has:
"WASHINGTON -- The National Academy of Sciences today announced the election of 72 new members and 18 foreign associates from 14 countries in recognition of their distinguished and continuing achievements in original research.
The election was held this morning during the business session of the 142nd annual meeting of the Academy. Election to membership in the Academy is considered one of the highest honors that can be accorded a U.S. scientist or engineer. Those elected today bring the total number of active members to 1,976."
http://www4.nationalacademies.org/news.nsf/isbn/05032005?OpenDocument