In Act I, Scene 3, we are introduced to the powerful relationship that exists between Juliet and her nurse when the nurse comments:
God mark thee to his grace!/ Thou wast the prettiest babe that ere I nursed:/ An might I live to see thee married once, I have my wish (I. 3. 63-66)
Juliet's "nurse," is, in fact, her surrogate mother, having nursed Juliet as a baby. Although it is not uncommon among aristocracy to use wet-nurses, the result of this practice is usually a strong maternal bond between the nurse and child. In fact, as we read the scenes between Lady Capulet and Juliet, as opposed to the scenes between Juliet and the Nurse, we note the stiffness, the formality in the relationship between mother and daughter, and the familiar, warm, informal relationship between Juliet and the Nurse. Quite naturally, the Nurse becomes Juliet's confidante and, by extension, becomes a prime mover in the plot to bring Juliet and Romeo together--taking messages to and from the couple; providing the ladder by which Romeo can get up to Juliet's room.
Juliet, of course, trusts the Nurse explicitly throughout the first part of the play, but after the death of Tybalt at Romeo's hands, the Nurse switches her alliance from Juliet to the Capulets, noting that Romeo has been banished. Her advice to Juliet is
Then, since the case so stands as it doth,/I think it best you married the county [that is, the count]./O, he's a lovely gentleman!/Romeo's a dishclout to him. . . . (III. 5. ll. 217-220)
Earlier in this scene, the Nurse tries to defend Juliet against the tirade of her father, Lord Capulet, and is attacked verbally in her turn (and perhaps physically), an indication that her maternal instincts still overpower her sense of self-preservation. But, in the face of Romeo's banishment--and his killing of Tybalt--the Nurse shifts her view of Juliet's marriage goals completely.
The question is, "What has happened to the warm, loving, intimate relationship between Juliet and the Nurse?" Although the answer is that no one is quite sure, one can argue that the Nurse, understanding that Lord and Lady Capulet now have politics and law on their side, decides to encourage Juliet to give up Romeo as a lost cause and give in to the marriage with Paris, which is by far the more rational choice of the two marriages.
During the Renaissance and later, marriage was often not based on love but on political considerations. In fact, marriage for love is a relatively modern construct. The Nurse's shift in alliance is not necessarily a betrayal of Juliet so much as it is a recognition of political and marriage reality. One can argue, of course, that the Nurse's abandoning of Juliet is an act of cowardice, and it certainly can be seen that way, but an equally strong argument rests on the political realities of the time, which would have made a marriage between Romeo and Juliet a nightmare--and short.