The conspirators are convinced from the beginning that Caesar is a serious threat to Rome. I would imagine that they would subscribe, without reservation, to the idea that governments should not be changed for "light or transient causes", as the United States Declaration of Independence puts it. Furthermore, they understood that Caesar was enormously popular, and therefore they felt that the only way to depose Caesar was to kill him, presenting the SPQR with an accomplished deed that they could then justify at leisure.
The flaw is that, in fact, they could not present a coherent justification when the time came. Brutus stands up before the people, confident that he will win them, and all he manages to say is that Caesar was ambitious. Mark Antony's rebuttal is the most famous speech in the play, but it wasn't a great feat. Brutus's justification is astonishingly weak, and supremely easy to rebut. Why doesn't Brutus present real reasons? It can't be that he didn't have any; he is honorable enough that if personal offense at Caesar's arrogance is all that he had, he wouldn't have acted. The premises of the play force us to accept that the threat to Rome from Caesar was real. Perhaps assassination was not the only option, but surely Brutus could have done better than just getting up on his hind legs and saying, "Uh, he was ambitious." Why did he not bother?
This difficulty makes it hard for me to see anything but an Idiot Plot here. The plot works because only because the characters are idiots.
The language is gorgeous, of course.
Now I'm starting King Lear, which a reader informs me is "harrowing".
Oh, I almost forgot to mention. I charged my Nook for the first time since I started Shakespeare on it. But that was in the middle of Cymbeline, 700 pages ago. 700 pages on one charge is not too shabby.