Vice-President Dick Cheney was in the white House the morning of Sept 11. He told the story of how the Secret Service came into his conference room and grabbed his shoulders and husteled him down to the underground bunker. He said he didn't think his toes touched the floor. Also, the First Lady, Laura Bush was in the white House also, she told how she was still in her bathrobe when the Secret Service came and got her. I don't think hitting the white House would have changed the Government's ultimate response in the long run, though in the short run, if the First Lady had been killed or injured, the President would have reacted earlier and the country would have suported him the same, if not even more so.