While 7am is very much during the rush hour, traffic from Dulles Airport to downtown DC gets a break--there are dedicated airport lanes that keep the drive to under an hour.
The problem is the expense of getting a rental car and then where do you park it downtown? Parking is very limited and quite expensive.
There is a bus that will take you from the airport to the Metro subway system, from where you can get into DC without the hassle of a car. Here's a link:
http://www.washfly.com/coach.html
By the way, you no longer can get inside the White House until you make a reservation, typically 90 days in advance, through your US Congressman's office.
I'd plan on it taking about 90 minutes or more from airport gate until you are on the National Mall.