What role does Macbeth's wife have in the death of Duncan? Did she push Macbeth into it?
Lady Macbeth certainly does push her husband to kill King Duncan in Shakespeare's Macbeth. In Act I:3, Macbeth realizes the way to fulfill the prophecy is to assassinate Duncan:
...why do I yield to that suggestion
Whose horrid image doth unfix my hair,
And make my seated heart knock at my ribs
Against the use of nature?...
This almost certainly suggests that Macbeth is thinking that the way to the throne lies in the killing of Duncan. But his wife is the planner of the couple, and she will plan the murder. She will also change her fickle husband's mind when he reverses his decision and announces, "We will proceed no further in this business" (I:7). She worries in Act I, Scene 5 that Macbeth is not ruthless enough to do what he wants to (kill Duncan), and her worries become actual when Macbeth does have second thoughts. She manipulates him by questioning his manhood, etc. and the assassination plot continues.
In fact, Macbeth's failures to stick to his wife's plans contribute to his downfall. When he kills Duncan's two attendants and orders Banquo and Fleance killed, he is exposed and his downfall hastened.
Lady Macbeth is definitely part of the plan to kill the king. In fact, you can argue that she is the one who first starts thinking about killing Duncan.
You can see this in Act I, Scene 5. When Lady Macbeth gets the letter from Macbeth telling of the prophecies, the first thing she thinks is how he does not have the drive to get to be the king.
Later in that scene, Macbeth comes home and tells his wife that the king is coming to stay and will be leaving the next day. It is Lady Macbeth who starts, at that point, to talk about making sure Duncan never leaves alive.
So, clearly, she is one of the major forces behind killing Duncan.