Cassius who, you will remember, was the one to convince Brutus to join this conspiracy in the first place, asks this question during the planning session at Brutus' house:
CASSIUS: But what of Cicero? Shall we sound him?
I think he will stand very strong with us.
The other conspirators agree. Keep in mind that, historically, Cicero is considered a wise man. He was a voice of reason in the Senate - he was known as the "great orator" because of his ability to give effective speeches and be persuasive. Clearly, to have him as part of the conspiracy will lend it some credibility.
However, Brutus will have none of it. This is his response to Cassius and the others:
BRUTUS: O, name him not; let us not break with him,
For he will never follow anything
That other men begin.
Brutus suggests that Cicero is too proud to follow in someone else's footsteps. Shakespeare has given us no evidence to suggest that this is true. In fact, in the previous scene, Cicero appears to caution against over-analyzing, which suggests that he is too humble to enforce his opinion upon a situation. This exchange does a few things in this scene. By showing how quickly Brutus dismisses the request, the audience can see that he has "taken charge" of the group. By his reaction to Cicero, we can see some element of jealousy or bitterness in Brutus, which tells us more about his character. Finally, by providing an example where Brutus is quick to decide, the audience is set up to see is Brutus' leadership will be successful or not. We see throughout that these decisions (such as choosing not to kill Antony) will come back to bite him.
caius cassius suggested to invite cicero to join the conspiracy
Cassius suggests that Cicero join the conspiracy against Caesar. In "Julius Caesar", line 142 of Act II, scene i, Cassius states that Cicero "...will stand very strong with [them]" (803), but Brutus quickly dismisses Caissus' suggestion by minimizing Cicero's importance as a co-conspirator.
Brutus' stand against Cassius establish him as the new leader of the conspirators. The conspirators trust Brutus' judgement and they believe him when he dismisses Cicero as an unworthy conspirator. Consequently, Brutus' motives change from honoable ones to ones based on selfishness. Brutus realizes that his new role as leader gives him an enormous amounts of power.