Nurse's responsibility in Romeo's and Juliet's deaths lies in the fact that she aided Juliet in helping the couple to marry secretly. We get the impression from the stories Nurse tells of Juliet in Act 1, Scene 3, plus how frequently we see them to together, that Nurse and Juliet are very close. Nurse would do anything to make Juliet happy. In fact, Juliet's happiness seems to be Nurse's one emotional drive, which explains why Nurse agrees to help Juliet marry Romeo in secret. However, the secrecy of their marriage, of course, leads to further complications later on in the play, namely, Juliet's father decides to marry her to Paris. The threat of having to commit a sinful, polygamous act in marrying Paris, of course, leads Juliet to fake her death, which further leads to both Romeo's and her own actual deaths. Had the couple waited to make their intentions of marriage publicly known, or had Nurse refused to go behind Juliet's parent's backs in helping them to marry secretly, both Romeo's and Juliet's lives might have been preserved.
Friar Laurence's responsibility for both Romeo's and Juliet's death likewise lies in secrecy and deception. While Friar Laurence may have been right in believing that Romeo's and Juliet's matrimonial unity might help put an end to the family feud, as we see in his lines, "For this alliance may so happy prove / To turn your households' rancour to pure love," he conducted the marriage in completely the wrong way (II.iii.94-95). He too would have been much wiser to refuse to marry the couple in secret but instead to encourage them to wait until they could let their intentions be known to their families. Again, the secrecy behind the marriage lead to Juliet's faked death, which ultimately culminated in both Romeo's and Juliet's real deaths.