In Act IV, Romeo has been banished and the Capulets are insisting that Juliet must marry Paris.  She is dead set against it, especially since she is already married to Romeo.  So she says she will do various things (mostly, various ways of killing herself) if those things will help prevent her from having to marry Paris.

For example, she says she'll kill herself in Act IV, Scene 1.

Do thou but call my resolution wise,
And with this knife I'll help it presently
God join'd my heart and Romeo's, thou our hands

A bit later on she talks about jumping off a tower.  She talks about being caged up with wild animals.  Anything but being forced to marry someone other than Romeo.

O, bid me leap, rather than marry Paris,
From off the battlements of yonder tower;
Or walk in thievish ways; or bid me lurk
Where serpents are; chain me with roaring bears;

Of course, later on she actually agrees to drink the potion that will make it look like she's dead.