The Biblical basis for claiming that Eve was created after the sixth day is one from inference instead of literalism.
The account in Genesis 1 starts with all the creatures first, then man on the sixth day. Chapter two continues on describing a different time of creation, or a smaller, second creation, if you will.
The story in Genesis two has Adam created separately, then God places him in the garden (verse 15). Then God decides that Adam should not be alone so he brings all the beasts to Adam to name them. Because of the wording, some literalists say that God made separate beasts right in front of Adam to be named; Adam then names all of them (verses 19-20).
Adam found none of the beasts suitable for his helpmate, so God put him into a sleep then made Eve from his rib (verses 21 -22).
The inference is that naming all the beasts would take a good deal of time. Even assuming that there were less kinds then there are today, seeing all of them, examining them, then deciding a name for all of those kinds would surely take longer than a day. Unless God brought the beasts to Adam in rapid fire succession, and Adam named them just as quickly, literalists holding this position insist that the event took a long time, much longer than a day.
Proponents of this view must neglect a literal reading of these verses, however. The final verse in Genesis 1, declaring the close of the sixth day, unmistakably puts the creation of mankind then. Takers of this view simply state that they are two separate stories with two separate lessons and neither is necessarily literal or more valid than the other.