Does Brutus have power in Shakespeare's Julius Caesar?

Brutus does possess power in Shakespeare's play, the power that political influence wields; however, he loses this power because of his ineffective idealism.

Brutus is considered a very influential senator, and for this reason Cassius "courts" him in order to gain his support in the plot to assassinate Julius Caesar. For, in gaining the support of Brutus, Cassius knows that others joining in the conspiracy will then follow through with action. Inflamed by idealism, Brutus is convinced by Cassius that Caesar will become tyrannical if given the single rule of Rome, so he joins the conspiracy to assassinate Caesar, providing the murder plot's needed influence and impetus to action.

Having thus joined with the others, Brutus strikes the final stab into Julius Caesar on the Ides of March. Brutus's idealism is not in harmony with the raw rules of life, rules Cassius understands and about which he tries to convince Brutus. Brutus, then, becomes flawed in his assessment of human nature and its motivations. His flawed judgment is evinced in his address to the plebeians. While Brutus initially elicits their support as they shout "Live, Brutus! Live, live!" after he explains that he killed Caesar, not because he did not love him, but because he loved Rome more— 

Had you rather Caesar were living, and die all slaves, than that Caesar were dead, to live all free men? (III.2.21-22)

Nevertheless, the crowd is swayed soon after when Brutus permits Marc Antony to speak. At first, Antony walks onto the pulpit, carrying the bloody body of Julius Caesar, and Brutus offers to slay himself if the crowd demands it. Instead, the crowd continues to shout "Live, Brutus!"

It is not long before Antony creates doubt in the minds of the plebeians that Brutus and the others may not be honorable, but are instead the ones who are ambitious, not Caesar. His presentation of Caesar's mangled and bloody body informs the crowd of a vicious assault, one more demonstrative of hatred and self-interest. The plebeians assume these wounds were inflicted by exigent men, not noble idealists. Brutus has been lying, these wounds seem to indicate. Thus, Antony makes of Caesar a martyr, not a tyrant.

Brutus's tragic flaw is his misunderstanding of the base nature of man, which leads to his loss of influence and the increased power of the more pragmatic Marc Antony and demise of Cassius and Brutus.