I just recently did the White House tour a few weeks back.
I organised the tour myself (I'm an Australian citizen) through Congresswoman Norton (District of Columbia). It may have helped that I submitted my application from my government email address, however I researched this and understand that she is the best opportunity for a foreign traveller to get a tour booked.
I submitted my application about five months out and received confirmation about two weeks before my tour date. Only had one minor issue when presenting my passport to security which was my birthdate was the opposite way to their list - a ten minute wait to confirm all is well and I was back in the queue for my allotted time - I did meet two other people who had the same problem, they were from England, so I would say this is somewhat of a common occurrence and nothing to be worried about if it happens to you when you arrive.
I thoroughly enjoyed the experience and I understand that in the last week, they have lifted a forty year ban on taking photos inside the White House.