Whether or not Mercutio holds any blame in Romeo's and Juliet's deaths is certainly a very interesting question. One of Shakespeare's main points is to show the consequences of all kinds of violent, uncontrolled emotions, ranging from both hatred to even love; plus, Mercutio certainly is one of the characters Shakespeare uses to portray uncontrolled emotions. Mercutio, much like Romeo himself, is characterized as rash and impetuous; plus, unlike Romeo, he is also characterized as having a rather fiery and hot-blooded temper. It is his rashness and his temper that helps perpetuate the fight with Tybalt, not only leading to his own death, but eventually to Romeo's and Juliet's deaths as well.
We especially see Mercutio's impetuousness and hot-bloodedness in Act 3, Scene 1, just before the fight with Tybalt begins. Practical, sensible Benvolio begs Mercutio to get off the street that day, warning:
The day is hot, the Capulets abroad.
And if we meet, we shall not scape a brawl,
For now, these hot days, is the mad blood stirring. (III.i.2-4)
But Mercutio refuses to listen, possibly because his own "mad blood [was] stirring." Prior to this scene, Benvolio informs Mercutio that Tybalt has challenged Romeo to a duel. Could it be that Mercutio feels angered by Tybalt's challenge on his friend's life? It's very likely that is one reason why Mercutio refuses to get off the street that day--he actually wants to be there and possibly even start a fight with Tybalt himself in honor of his friend. However, remaining on the street to provoke a fight is an extremely rash and impetuous decision of Mercutio's.
Mercutio further shows his impetuousness and hot-bloodedness when he becomes angered by Romeo's attempts to pacify Tybalt rather than answer his challenge. Mercution becomes so angered by Romeo's attempts to just walk away from Tybalt that Mercutio declares, "O calm, dishonourable, vile submission!" and challenges Tybalt to a duel himself (72). However, Mercutio's rash, emotionally driven response is a poor response, not only because fighting on the streets breaks Prince Escalus's newly decreed law, but also because it leads to his own death. More importantly, Mercutio's rash, impetuous response incites Romeo to make his own rash, impetuous decision to avenge Mercutio's death. Romeo's own poor decision of course leads to his own death as well as Juliet's. Hence we see that Mercutio embodies Shakespeare's point concerning the consequences of violent, uncontrolled emotions, especially emotions led by rash, impetuous decisions.
I believe both were very responsible. The nurse facilitated Juliet getting out of the house and the friar did not get to Romeo in time to tell him that Juliet was not, in fact, dead, but would awake some time later.