It is important in considering this question that the student be aware of some facts about Julius Caesar that are not contained in Shakespeare's play. For one thing in 60 BC, Caesar, Crassus, and Pompey formed an alliance that dominated Roman politics for years. While they were opposed by a conservative faction, Caesar's military prowess won him great acclaim for his accomplishments, such as conquering Gaul and later Britain. In fact, these accomplishments threatened to eclipse those of Pompey, as well. When the Senate ordered him to lay down his military command after the Gallic Wars, Caesar defiantly refused.
Now, as is mentioned in the play, Caesar defeated Pompey, who had been his ally, in 48 B.C. In Act I, Scene 1, Marullus alludes to Pompey, asking the people why they now support his murderer, Caesar:
And do you now put on your best attire?
And do you now cull out a holiday?
And do you now strew flowers in his way
That comes in triumph over Pompey's blood?
There is further information in Act I that is, indeed, cause for concern about Caesar's desire for the absolute power of an emperor. For instance, according to Cassius, when Caesar enters the city of Rome, Marc Antony offers Caesar a crown, which he refuses, but when offered it the third time, he appears desirous of wanting it to remain upon his head, according to Casca:
...and, as I told you, he put it by once; but for all that, to my thinking, he would fain have had it....And then he offered it the third time. He put it the third time....(1.2. 243-245)
Moreover, Caesar's own powerful ego manifests itself in the first scene as he alludes to himself in "royal terms," clearly indicating his desire to be an absolute ruler:
I hear a tongue shriller than all the music
Cry 'Caesar.' Speak. Caesar is turned to hear" (ll. 19-20).
This reference to himself as Caesar belies his confirmation of his own power, for he is, as he himself says, "always Caesar."
Were, then, the concerns of Cassius, Brutus, and others that Caesar may usurp absolute power justified? Indications in Act I of Caesar's ambition and his predilection for absolute power in his previously defying the Senate and slaying his ally Pompey point to Caesar's tyrannical nature. And, after Caesar has entered Rome in triumph, fondly holding the coronet upon his head when it is offered to him, Casca interprets this action as indicative of Caesar's desire to become emperor. Likewise, Cassius perceives Caesar as a Colossus under whose legs "we petty men" walk, he says. Nevertheless, despite all these indications of Caesar's great cupidity and desire for power, Cassius has his judgment marred by envy and Brutus is inflamed by his idealism as he wonders if Caesar will long be just and honorable if he is given the authority of kingship.
Because their judgments are flawed by their emotional responses--envy and idealism--the concerns of the conspirators are presumptuous. Brutus certainly exerts poor judgment in his declaration that he has come to his decision because Caesar is like a "serpent's egg" that, if left to live, may hatch and "grow michievous." Indeed, the cost of subsequent civil war after Caesar is slain points the greater dangers that followed the assassination of Caesar.