I think that both Romeo and Juliet say things in this act that show that they would rather die than be separated. For Romeo, there is a good quote in the lines he speaks to Friar Lawrence in Act III, Scene 3. He says
To me, what he's saying is he'd rather die than be exiled. Juliet seems to feel the same way. In Act III, Scene 2, she says to the nurse (when she thinks Romeo, and not Tybalt, is dead)
To me, this means that she wants to be buried with Romeo in one coffin (bier).
Both Romeo and Juliet make such a claim to Friar Lawrence after learning of the Prince's sentence of banishment for Romeo's slaying of Tybalt. Of course, banishment spurs the fear that Romeo and Juliet will never be able to see one another again.
In Act III, Romeo states:
Hence-banished is banish'd from the world,
And world's exile is death: then banished,
Is death mis-term'd: calling death banishment,
Thou cutt'st my head off with a golden axe,
And smilest upon the stroke that murders me.
And Juliet, not to be outdone, then questions Friar Lawrence about any possible remedy to Romeo's banishment:
Tell me not, friar, that thou hear'st of this,
Unless thou tell me how I may prevent it:
If, in thy wisdom, thou canst give no help,
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;
And ere this hand, by thee to Romeo seal'd,
Shall be the label to another deed,
Or my true heart with treacherous revolt
Turn to another, this shall slay them both:
Therefore, out of thy long-experienced time,
Give me some present counsel, or, behold,
'Twixt my extremes and me this bloody knife
Shall play the umpire, arbitrating that
Which the commission of thy years and art
Could to no issue of true honour bring.
Be not so long to speak; I long to die,
If what thou speak'st speak not of remedy.
Both Romeo and Juliet are willing to die rather than suffer through banishment and not being able to be together.
In the scene that Juliet learns of Romeo killing Tybalt, she expresses that she is more hurt by the fact that Romeo is being banished and says:
Wash they his wounds with tears: mine shall be spent,
When theirs are dry, for Romeo's banishment.
Take up those cords: poor ropes, you are beguiled,
Both you and I; for Romeo is exiled:
He made you for a highway to my bed;
But I, a maid, die maiden-widowed.
Come, cords, come, nurse; I'll to my wedding-bed;
And death, not Romeo, take my maidenhead!
Here Juliet is saying if she can't be with Romeo, she'd rather die than let any other man have her.
Later in scene iii, Romeo confesses willingness to kill himself figuratively:
As if that name,
Shot from the deadly level of a gun,
Did murder her; as that name's cursed hand
Murder'd her kinsman. O, tell me, friar, tell me,
In what vile part of this anatomy
Doth my name lodge? tell me, that I may sack
The hateful mansion.
Drawing his sword
Here, he was asking the friar where and how he should kill himself for the wrong he has done to Juliet by killing her cousin.
Both Romeo and Juliet show their desperation in these scenes. Their willingness to kill themselves shows the passion they must have had to be together.