What future event might the line "My grave is like to be my wedding bed" hint at in Romeo and Juliet by William Shakespeare?

This line foreshadows the fact that being in love with Romeo will be Juliet’s doom.  The line is spoken when Juliet first sees Romeo at the Capulet ball.  She does not know who he is, but makes this rather profound statement, which seems to imply that if Romeo is married, she will never marry. 

Juliet asks Nurse his name, and she explains that Romeo is a Montague. 

Nurse

His name is Romeo, and a Montague;
The only son of your great enemy.

JULIET

My only love sprung from my only hate!
Too early seen unknown, and known too late!
Prodigious birth of love it is to me,
That I must love a loathed enemy. (Act 1, Scene 5) 

This is significant because the Montague and Capulet families have been feuding for ages.  Juliet does not want to get in the middle of the feud and betray her family by loving a boy from the wrong family.  She bemoans the irony of it. 

Of course, Romeo and Juliet do marry, in secret.  Her prophecy seems to be coming true.  She will die soon after marrying Romeo.  She did not exactly mean it this way.  She thought that she would die without marrying. Instead, she married and her death was a direct result of marrying in secret. 

Before he died, Romeo made a speech that seems to echo Juliet’s earlier words about her marriage bed being her tomb.

Ah, dear Juliet,
Why art thou yet so fair? shall I believe
That unsubstantial death is amorous,
And that the lean abhorred monster keeps
Thee here in dark to be his paramour? (Act 5, Scene 3) 

You know the story.  Juliet faked her death to avoid marrying Paris, and Romeo did not get the message.  He came back and saw her, thinking she was dead, and poisoned himself.  She woke just in time to see that he was dead, and killed herself.  It seems that fate was unavoidable for them.