Al Queda stage ground assault on White House on 9/11

Having watched Olympus has Fallen and White House Down, would it have been possible for Bin Laden to have gathered a few extra followers in the US to attack the White House at the same time as the WTC and Pentagon were hit with hijacked planes ?

Lets say suicide bombers attack the front gates and fences and allow several vans loaded with armed fighters to storm the grounds. Would they be able to force their way past the Secret Service and into the building itself ? Doubtful but is it at least improbable rather than impossible ?
 
can vans get close to the White House? I thought that after the attack on the Marine barracks in Beirut, the WH had the entrance to it's gates rearranged to prevent such things...
 
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