The open memorials like this one don’t close according to the national park service.
>>The public may visit the World War II Memorial 24 hours a day. Rangers are on duty to answer questions from 9:30 a.m. to 11:30 p.m. daily and to provide interpretive programs every hour on the hour from 10:00 a.m. until 11:00 p.m.<<
The website comes by way of the wayback machine because the park service website is partially down.
http://web.archive.org/web/20121108195139/http://www.nps.gov/wwii/planyourvisit/hours.htm
Good catch from the wayback machine!
The spiteful little thing in the White House is just using this as an excuse to vent his spleen on a group that he perceives as being insufficiently awed by him.