I disagree with the above post. I don't think Elizabeth was trying to make John feel guilty about his marital infidelity. She is clearly hoping to impress him with her cooking in Act II, as she says that she "took great care" with the rabbit stew; she also tells him that the "magistrate sits in [his] heart that judges [him]," and that she does not. And we know that she cannot lie. To me, Elizabeth seems to be motivated by the desire to get her relationship back on track -- though she struggles to trust her husband again -- and for the trials to end (and for Abigail Williams to be known for the liar that she is). It is she who prompts John to go to the court and tell them what Abigail told him -- that Betty's illness has nothing to do with witchcraft -- though he is reluctant.
John's motivation, on the other hand, changes throughout the play. Initially, he is concerned with not only getting his marriage back on track (as is his wife) but also with protecting his reputation. He doesn't want to have to share the news of his sin with the community, and so he is reticent to expose Abigail as a liar. He becomes angry when Elizabeth continues to insist that he should go to town and tell the court what Abigail told him. Later, however, in Act III, the motivation to save his wife trumps his concern for his own reputation, and he confesses his lechery in an attempt to prove Elizabeth's innocence and Abigail's treachery. In Act IV, John is motivated first by a desire to save his life and then, finally, by a desire to retain his integrity. He considers confessing a lie, and actually does it at first, because he wants to go on living and to be alive for his family. However, he eventually comes to the realization that it is possible for him to retain integrity and, to do so, he must be willing to die for it.
Elizabeth's motivation changes over the course of the play. At first, as a reaction to her jealousy for John being seduced by Abigail, Elizabeth's motivation is to make him feel terribly guilty for what he has done. But as the play proceeds and she is accused, her motivation is just to get to be with him. In fact, against her Puritan faith, she lies in court about John's lechery, thinking that he would have lied. She lied to save his reputation. As the play just about closes her motivation becomes to see John feel free. He struggled with whether to sign a false confession or not.
John's motivation remains fairly constant: to find falsehood and expose it. John Proctor is one of the most forward and blunt characters ever written. With his wife, as she tried to make him feel guilt, he made sure she understood her cold nature may have prompted his cheating. With the court, he sacrificed his own reputation to point out the falsehood of the accusations that Abigail was making. Furthermore, he used the truth of the Putnam's situation to prove why they may have encouraged the girls to pretend. By the end, he refuses to save his own life with a simple lie. He would die to demonstrate the truth.