Eilzabeth is pregnant by this point in the story. It is only possible that this is John's baby. Even though John and Elizabeth's relationship has been rocky, having a baby together should be a joyous opportunity for them. This very information might not only give John a reason to live for himself, but a hope to live for two others: Elizabeth and the baby.
Danforth is hoping that this information can manipulate John into a plea. He wants to see John admit to witchcraft just to guarantee that John can continue to live. What Danforth does not realize is John's strength of character. In fact, I don't think John realized how strong he is. John ultimately makes a decision in spite of the fact that Elizabeth is having a baby, but it was certainly a position worth Danforth's time to have John consider. Any father would want to be there for his child especially when a previous infidelity had inhibited his relationship with the woman he loves.