I'm not sure if the American people couldn't be more outraged. 9/11, as horrendous and tragic as it was, hit the base of U.S. financial and military power, but not government power.
If the hijackers on Flight 93 were successfulin hitting either the White House or the Capitol (assuming that the it wasn't shot down first), then the American people would be baying for blood even more that OTL. It would be the first time since the War of 1812 that Washington D.C. had been directly attacked. Now add to that the fact that you would potentially be killing government officials, and all bets are off.
The government would continue to function as President Bush was in Florida at the time. I guarantee that he won't be returning to Washington for a few days; though with modern technology, he can govern from nearly anywhere. If the Capitol is hit, Congress will conduct its business elsewhere until the damage can be repaired; if the White House is hit, the President will stay in Blair House. Concerning the former: elections (in the case of Congressmen) or appointments (in the case of Senators) would quickly happen to replace those killed.
World opinion would definitely be more resolute for the U.S. (Saddam may not be so stupid as to gleefully boast of the success of the attacks). You might see an even more draconian (opinion based) PATRIOT ACT. Commitment to the War on Terror would probably be stronger amongst the public for somewhat longer. There would definitely be huge butterflies depending on what lawmakers were killed.