From what I heard on the news, some of the hijackers were in the US on expired visas, and they had even traveled out of and back into the US a few times on their expired visas.

One of the hijackers was stopped while driving. When asked for his driver's licence, he said he had left it at home. He was given a ticket and ordered to appear in court. Prior to the court date, he obtained a legitimate, legal, US driver's licence (while living in the US on an expired visa), and when he failed to show up for the court hearing, a bench warrant was issued against him. I don't know how much time passed between the issuance of the bench warrant, and the hijacking.