They have plenty of fighter jets nearby.
There are atleast 20 military bases that could have gotten fighter jets there within 15 minutes.
But there are jets right in DC that are specifically there to defend the White House, Pentagon, Congress etc. that like you said could have been there in a minute.
Usually when I'm in DC I will see some fighter jets in the are during the day. From what I understand they keep some in the air nearby all the time.
While investigators pieced together evidence, two former Florida flight school students were identified by German authorities as terrorists aboard the two planes that smashed into the World Trade Center.
Hamburg investigators said Mohamed Atta, 33, and Marwan al-Shehhi, 23, had studied at the Technical University in Hamburg and had passports from the United Arab Emirates. Both men received pilot training at Huffman Aviation, a flight school in Venice, Fla., where FBI investigators are examining student records.
FBI investigators learned that Atta and al-Shehhi also took two three-hour courses at SimCenter Inc. in Opa-Locka, said Brian George, son of flight school owner Henry George.