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The solution makes less and less sense the more I think about it.  If there were ten people, five with brown eyes, five with blue, and someone said "I see someone with blue eyes," it doesn't help them at all.  Five of the green eyed people would know that already, and so would four of the blue eyed people. 

But if the people don't know what color eyes they have, the blue eyed people can't all of the sudden just realize after five days "Hey, the other four blue eyed people haven't left, so I must be one of them!"  None of the others know their own eye color, because they haven't had any means of figuring it out.  So why would they assume that they themselves had blue eyes?

And what about the brown eyed people?  Why wouldn't they assume that they had blue eyes if they saw that all these blue eyed people weren't leaving?  Where do they come into play here?

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I can't wrap my head around how the guru's statement suddenly spurs them into action either, but the reason the brown-eyed people don't play a part is because they always require one more iteration: if there are n blue-eyed people, brown-eyed people see them all, but the blue-eyed people can only see n-1 people with blue eyes, hence reducing the trial-and-error process by one day.

Suppose that there was only one blue-eyed person. When the guru says that he sees at least one blue-eyed person, each of the brown-eyed people considers that he, too, has blue eyes, but since the blue-eyed man knows he's the only one he's gone the following day and the brown-eyed people give up. With two blue-eyed people, they both see that the other has waited a day, and since no other blue-eyed people are around they know they both have blue eyes. Brown-eyed people still need to know whether or not they happen to be the lucky third one, but alas, the two are gone the following morning.

I have a solution. At 11:55, everyone rips their eyeball out and looks at the color and leaves on the ferry at 12:00, and while on it they get help from doctors.

Oh!  I get it now!  Thanks Omcifer and Kentona. 

The reasoning behind everything is still a bit shaky, and I'm still not sure why what the guru says makes any difference.  There must be something in it that I'm just not getting. 

The importance of the guru

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The gurus words give insight into the other persons eye color. Pretend there is only 1 blue eyed person on the island. He is unaware he has blue eyes until the guru says "I see someone with blue eyes" and he realizes "Hey no one else has blue eyes." The same holds true then for 2 people. Person A and B have blue eyes. A and B know that there are 100 number of brown eyed people and at least 1 blue eyed person, the one opposite themselves. They can't use the logical solution of the riddle until the guru says "I see a person with blue eyes." Before this A may have counted 100 browns and 1 blue but he may have had red eyes. Person A knows that when the guru provides the statement, that if person B was the blue eyed person on the island, he would now be aware of it. Without the words, Person A could not be aware of what person B is aware of because he neither knows their own color.[/spoiler]
This makes sense to me but I might be able to give a better explanation. The guru is necessary though.

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My problem with this is that as soon as there is more than 2 people with blue eyes, this no longer holds up, because no matter whether you have blue eyes or not, you are sure that every other person with blue eyes can see one other blue-eyed person (since you yourself see at least two blue-eyed island dwellers, so no matter whether or not you yourself have blue eyes, you know that all other blue-eyeds see at least one other). I see the logic when there is one or two people with blue eyes, but it seems like it no longer works with three or more.

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Think of the case with three people. Each one of the blue eyed's sees two other blue-eyed. As far as they know there are only two other blue-eyed people here, and as far as they know, each of these two blue-eyed people only sees one blue-eyed person. Since they're perfect logicians they know how the other ones would think, and when they don't leave on the second day, it can only be because there's a third blue-eyed person - me.
  To put it in mathematical style, each person in this case views a system of two blue-eyed persons. When the system doesn't work, it's must be because the other two blue-eyed ones are not seeing the system you are seeing - you're watching two of 'em, if there was only two, each of them would only see one. But they don't, so there must be more people. and there can only be one more, you.

Now think of the case with four people - the fourth person is viewing a system of three people. When they don't leave on the third they, it's because, in the same way, there must be more than three people. With five people, if the four other people don't leave on the fourth day, there must be five people. And so on - with N people, if the other N-1 people don't leave on the N-1'th day, there must be N people.

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We know that, we are not debating the solution, but rather the usefulness of the guru's revelation when there is at least three blue-eyed people. We know it still works with three or more people, but not if the gurus' revelation stays useful to the island dwellers.

Correct answer:

They wouldn't leave...

Chuck Norris wouldn't let them.