'Wisely and slow, they stumble that run fast', says Friar Laurence to Romeo. And he might just be right. The haste enters the play with the meeting of Romeo and Juliet (before that it's been a rather slow build to the Capulets party and a lot of exposition).
Romeo turns back from leaving the party in order to immediately find Juliet at her balcony (or her window... stage tradition is a powerful thing): before he leaves her later that morning, they have already vowed to be married, and, before lunchtime, Romeo has Friar Laurence agree to marry them the same day.
Yet what actually precipitates the tragedy itself is the death of Mercutio and Romeo's murder of Tybalt which follows it - and it's perhaps the impulsiveness of Romeo which causes him to murder Tybalt, as Benvolio says, before anyone could draw a sword to stop it. So the haste rushes the play onto its crux point (the lovers, are, of course, 'death-mark'd') but it's perhaps Romeo's personality that twists a comedy toward tragedy.
Though Friar Laurence's plan to save the day only fails because of a letter which Friar John is unable to deliver: if you read what Friar John says, he claims a plague stopped him from being able to inform Romeo that Juliet is not really dead. Romeo then kills himself because he thinks she is dead: and then, well, vice versa.
So in the end, is it a tragedy of haste? Not really. It's more a tragedy of fate - or, if you like, of bad luck.