Any terrorist with a few thousand bucks and a non-commercial pilots license has a shot at blowing up the White House. The only thing stopping this is a largely secret (for good reason) air defense system in the Washington DC area. There is a 48 kilometer no-fly zone around the White House. Any aircraft entering that zone without permission is a potential suicide attacker and liable to attack by, well, no one knows for sure.
The easiest aircraft to obtain for an attack would be a two engine type like the Piper Aztec or Cessna Businessliner. You can rent one of these for under $500 an hour, or you can buy one second hand for under $300,000. You have to know how to turn off any air traffic control transponder the aircraft might be equipped with. This makes it much more difficult for the air traffic control system to track you. These aircraft can carry about 500 pounds of explosives (turning them into the destructive equivalent of a Tomahawk cruise missile), and are fast enough to breach the no-fly zone and hit the White House in eight minutes. That doesn't leave enough time to get F-16s into the air and in position for an interception. There are said to be Stinger crews in the White House (or personnel trained to use Stingers.) But firing the Stinger from the White House is a tricky business, as there is less than a minute between the time the approaching aircraft comes into range and it hits the White House (unless the missile takes out an engine and forces the aircraft to land somewhere else.)
There are said to be some UH-60s stationed in the area, armed with M-16 assault rifles, and ready to get airborne in minutes. These choppers intercept several aircraft a week that have entered the no-fly zone. But these helicopters are there mainly to protect the White House from Congress (as in "what are you doing about all these unauthorized aircraft over Washington.") In the last two years, no aircraft has made a suicide run at the White House. The helicopters could also be equipped with Sidewinder air-to-air missiles. The Sidewinder has a range of six kilometers and has been mounted on helicopters for years. There were also reports of Army Avenger systems (a hummer armed with Stinger, a heavy machinegun, radar and laser range finder) in the area, as well as Stinger missile teams. The Stinger has a range of only 4.5 kilometers. Effective range of the .50 caliber machine-gun is more like two kilometers. There could also be teams of snipers equipped with .50 caliber rifles (firing armor, or engine block, piercing incendiary bullets). These could also take down one of these aircraft, or at least disable the engines and ruin the attackers aim.
Before you can knock down a suicide aircraft, you have to be able to track the intruder, and if the pilot comes in at tree-top level, that will be difficult. Flying like that within the DC area suburbs is also dangerous, for there are numerous office parks within that area, many with buildings over a hundred feet high. But the no-fly zone is 1800 square kilometers, and each Stinger team is only covering about 14 square kilometers. The Avenger can move around, if it doesn't get stuck in traffic, but is unlikely to be able to cover more than a kilometer (or two) a minute, while trying to get in position for a shot. Because of their short range, the Stingers could only be used as a last line of defense, and would probably be stationed within 5-10 kilometers of the White House. While the attacker could further complicate the situation by coming in at night, this makes it more likely to collide with some high rise obstacle that is not well enough lit.
The U.S. Army is in charge of air defense on land, and has apparently devoted considerable thought and study to the problem. A workable solution is going to require a lot of equipment, weapons and troops. And also a lot of secrecy. There will have to be tight coordination with local Air Traffic Control, and military radar systems as well. There are even more exotic radar systems that might be brought into play.
So whatever the air defenses for the White House are, it will be a long time before we find out what they are. Unless there is a successful attack, in which case the details will come out in the investigation that follows. So far, there have been over a hundred small aircraft that have wandered into the zone by accident, or gone there for thrills. No one has been shot down. But, then, no one has really tried to take out the White House. Yet.