In this excerpt, the word that most resembles the meaning of "egregious" is "scandalous." The excerpt implies that whatever mistake the speaker made, it was a very obvious and very bad one. She also states that she wishes someone had stopped her from making such a bad mistake, but that her husband found it hilarious.
The repetition emphasizes Johnson's belief in justice, and he guarantees to the American people that he will do everything in his power to ensure equal rights for all.
