I just did and spoke to someone who had clearly heard the message from others, although she said they are not allowed to say if they are getting lots of calls.
White House switchboard: 202-456-1414
(or White House comments: 202-456-1111)
The wait to speak to a person was refreshingly brief and hurray: no muzak or canned message while on hold !
How many volunteer message takers are there, I wonder...